Looking for help from someone experienced in examining US Army records from the War of 1812!

A few months ago I made [this post], and I am hoping I can get some help with it. Frankly I think it is ridiculous that my x4 great grandfather's father, older brother, and younger brother are all documented as having served in the exact same company of the exact same regiment during the War of 1812, but that the man bearing his same name documented as serving alongside them wouldn't be him.

Still, however, I have to entertain this possibility that it's a coincidence, because the US Army discharge files document that the man of that company and of that regiment who enlisted on the same day as at least two of them and who has the exact same name as my x4 great grandfather...died. But my x4 great grandfather died the decade after, so something's amiss there.

I would really appreciate any feedback or insights, and I'm really looking forward to hearing what others have to say about this fascinating case!