The famous book Stolen Valor proves beyond a shadow of a doubt that the fake veteran subculture exists.
And you really can write anything you want on an FEC form. Every election cycle sees donations made by foreign nationals claiming to be US citizens, such august individuals as Seymour Butts and Ben Dover making donations, etc.
Plenty of people make donations listing a different employer because they don't want their employer to know who they are contributing to: i.e. Jim Jones who works at Acme has a supervisor who is a gung-ho leftist and is afraid that if he donates as Jim Jones of Acme his boss will find out - so he donates as Jim Jones of Worldwide International instead.
Notice Mark that the poster offered no contrary evidence.
That there is a subculture of fake veterans isn't an issue, and wasn't your question.
The poster has no proof.