It does appear that Stephen B was a Capt in the 77th EMM active for 53 days in 1863 Co H "Detached"
His father was a bit of a stinker per the PM file:
Elkins, Philip D. Unknown Atchison, KS Elkin required to take Oath and report weekly since he was unable to give security; Graham letter used to demonstrate charges against Elkin 08-23-1864 F1311
Elkins, Philip D. Unknown Atchison, KS Elkin required to take oath and report weekly; letter to editor from M. Graham, Jackson (County) MO re: open rebels in city who planned to redeem Westport and Kansas City from Republicans and wipe out KS ??-23-1864 F1311
Elkins, Philip D. Unknown Atchison, KS M. L. Graham writes that Elkin was rebel back to 1856, raised rebel flag here and Kansas City; at Wilson's Creek and Lexington; other rebels Ben Newson, Alex Strut, Geo. Baker, Geo. D. Foglesong 08-12-1864 F1311
Elkins, Philip D. Unknown Atchison, KS Oath; description: 6', age about 56, sandy whiskers, large size and well built, heavy eyebrows, hair thin 08-17-1864 F1311
I think the confusion lies with the mis-quote and poor reporting on Wikipedia. If you read the entire entry of the interview in The Centennial History of Missouri it does not appear to me that Elkins relates he was in charge of Co H, 77th EMM at Lone Jack. I find his words to ring true and suspect the "historians" have not kept his story straight as they have retold it. Clearly his run in with Quantrill and company makes sense and clearly is related to being early in the war prior to his EMM service. As to Lone Jack he clearly states that the Confederates won the battle and took the field, identifies the combatants correctly and his post battle story matches very well with others of the day. From the tone and referral to a "Union regiment" as well as his definite hedging as to how he ended up in the EMM in December and his mention of being a "marked man" I suspect he was at Lone Jack as a CONFEDERATE. With that in his background I could easliy see how he might not have been transparent but being a good parser of words he relates "while in the service" I was at Lone Jack. He just doesn't say which side and lets the reader assume its while in the service of the Union. Also have to remember he quickly made tracks for New Mexico at the end of the war and did not stick around NW Missouri, otherwise known as protecting one's hide after the war.
From "Centennial history of Missouri: (the center state) one hundred years in the Union, 1820-1921, Volume 2"; The S. J. Clarke publishing company, 1921 pg 628 - 630.
War Experiences of Stephen B. Elkins.
When Stephen B. Elkins was secretary of war in the Cabinet of President Harrison he told how the war in Missouri divided his family. Elkins graduated at the State University in 1860. The address to his class was by Sterling Price and the theme was devotion to one's country.
"My father left everything and went into Sterling Price's army; my brother John, who should have gone to college, succeeding myself, wheeled about and instead went into the Rebel army at 16. I met him on the prairie when the first horns of the war blew, carrying a gun at his saddle string, and he said he was going to kill the Yankees. Said I: 'J°hn, you won't be out three weeks before you will wish you were home in your mother's bed; there is no excuse for going to war against the government. Everything I have read and reflected teaches me that.' He said he would not discuss the question; that he was going to kill some Yankees. Afterward he told me that when he got into the first fight around Lexington, Mo., and bullets commenced to fly past his ears, he did wish he was home in his mother's bed. Had he been educated he would have made considerable of a man, and probably would have been governor of Colorado, in which state he arrived at distinction, being a state senator before he died. My brother surrendered with Dick Taylor at the close of the war in Louisiana. My father never came into the new situation gracefully."
Before he joined the Union army Elkins had a thrilling experience with the guerrillas:
"I was going along the road one day when I came upon three men wearing the Yankee •blue, playing cards at the roadside. One of them said: 'Them boots is too good for him;' another said, 'I am going to have his jacket.' I thought I should be shot right away. Those fellows cared nothing more about taking a man's life than killing a rat or a cat. I asked them to take me to their commander. They marched me along and we got to Quantrell's camp. There I saw Cole Younger, Dick Yager and Todd, and several others afterward known for.desperate deeds. Those I have mentioned were farmers' sons around where I lived. They identified me and said: 'Here comes Steve Elkins.'
"All the way along I had been afraid that those fellows who had captured me would shoot me in the back, for I had on the watch which I am carrying now in the office of the secretary of war. Those boys said that I must be all right, as my father and brother were in the Confederacy; that I myself was a little off on the subject, but must come right at last, etc.
An Intimate View of Quantrell.
"I asked them to show me Quantrell. I took a look at him. He had dark sandy hair, the eye of a leader, was young and wiry and taciturn. Said I, 'Boys, where is he going to take you?' 'We never know,' said Younger and Todd. 'He never tells anybody where he is going.' They started out in an hour or so with no order given but 'saddle up,' which spread around, commencing with Quantrell's lips. I told these persons not to be in a .hurry, but let the others go on. 'Now,' I said, 'let me go home to mother, as there is nobody to look after her. Father has gone off with Price and somebody must take care of her.' So I started off on my horse, which I had been allowed to keep, and as soon as I got to the first foliage you can be sure I went fast.
"The next time I saw Quantrell he had come with a part of his band to a farm house where I was stopping. Those fellows were perfect dare-devils. The moment they were called to halt they were down, with their horses tied, singing, dancing, playing cards, reviving the sports of the buccaneers. Being in the house. I thought I had better put on a bold face, and I went to where they were getting dinner and exchanged some words with Quantrell. He was not a large man, but you could tell that he was a leader.
"I had a hard experience staying at home at the commencement of the war. There was nowhere else to go except into the army. I can hardly tell now how I drifted to the opposite side from father and brother. I suppose that it was education; a disposition for peace, instead of fighting. I finally entered the militia, and we had a meeting and formed a company of which I was elected captain. • Kansas City was the only place in Missouri then that had Union people in it, at least in that part of Missouri. The colonel of the regiment to which I became attached was Kersey Coates, who built the big opera house and hotel in Kansas City. I was in continual danger of being killed, and was marked by Quantrell's men as a renegade who was to be shot as soon as taken. I saw one battle •while in the service, that of Lone Jack, and a most awful battle it was. Col. Emory S.Foster had a Union regiment which was attacked by the brother of Senator Cockrell, but Foster thought the Confederates were the guerrilla bands who raised the black flag, and never gave any quarter. So he refused to surrender, and every one of his officers was picked off. The guerrillas were victorious. I went over the battlefield afterward, and
the blood, the cries for water and death, the naked bodies stripped of their clothing, the dead horses which served for ramparts, gave me a disgust for war, which makes it seem strange that I am here at the head of the war department of this great government."