Polk acted on his own. He was not authorized by the Confederate government to cross the Mississippi River from Missouri and occupy Hickman and Columbus. After Polk did so, Davis excused him by saying the necessity justified the action. Walker, on the other hand, ordered him to get out of Kentucky. Not only did Polk stay put, he created a fortress at Columbus.

Polk did not occupy Hickman and Columbus and move troops farther east into Kentucky as a response to the Federals' recruiting and training men at Camp Robinson, nor was his action a response to the Federals' seizing boats on the Ohio or any other river, nor was it a response to any other minor Federal presence in Kentucky. He did it because he had learned it was Fremont's intent to seize Columbus. Polk saw the value of occupying the high ground above the river. He saw the value of blockading the river. He installed batteries and a huge chain across the river. Polk's own words, quoted earlier, revealed his intent, which was to be ahead of the enemy. He didn't give a hoot about Kentucky's neutrality or anything else the Federals had done earlier in minor violation of that neutrality. He saw the value of controlling the Mississippi River below Cairo, and he wanted to grab that control before the Federals did. He also saw the value of controlling the mouth of the Tennessee River, and that's why he wanted to be ahead of the Federals in occupying Paducah.

I don't see that one side having a training camp, whether armed or not, and seizing contraband-carrying boats on the rivers, and the other side aggressively occupying two towns with armed forces, deploying other armed forces farther east into Kentucky, and blockading the Mississippi as being remotely comparable in degree. The Federal offense pales in comparison to the Confederate offense. When Davis said the necessity justified the action, he wasn't talking about responding to the minor Federal presence in Kentucky. He was talking about preventing the Federals from controlling the Mississippi below Cairo.

Since you don't seem to accept my degree point, let me try an analogy with you. In the mid-1950s up to May 1960, the US flew U-2 aerial photography missions over the USSR. Obviously, that was a violation of the USSR's air space. But the degree of that offense was minor in comparison to dropping down and occupying Moscow. And that's borne out by the response. The airspace violation resulted in the Soviets' shooting down a U-2 plane and temporarily holding the pilot. Occupying Moscow would have resulted in nuclear war. The degree justifies the response.

When John Y. Simon said the Confederates were first to violate Kentucky's neutrality, he was talking about the degree of the offenses. The Federal violations were minor in comparison to the Confederate violation. But that doesn't really matter because Polk was not in Kentucky in response to the Federals' being there in a minor way. He was there to be ahead of the enemy in controlling the rivers.