THere are at least two parts to this puzzle, and you're holding one of them. The pension application you mentioned should include notes as to why the soldier's claim was denied. Since Federal service files are much more complete than theor Confederate counterparts, denial of a claim may well mean that Bradley never joined the unit in question. It would depend on the details (incorrect, missing or accurate) he provided in making the claim.

Not having seen the claim, I can't really offer a good guess.