To add a little more to this:
Nimrod Smith, the one I can't find a service record for, applied for a pension May 23, 1929, which is kind of late, don't y'all think? So if he lied about his service just to get a pension, wouldn't you think he would've applied for it much sooner? Was knowledge of pensions common? I suppose he could have just learned about them in 1929 and made up all the stories at that time. He was about 15 or 16 when he supposedly enlisted and was about 82 or 83 when he applied for a pension.