In the US, it is now illegal to claim to have military rank or awards you have not earned.
As a veteran, and a member of a veterans' organization, my experience has been, the more one talks about what they have done, the less likely they will have done them. Most veteran's will discuss what they have done, if asked, but they will not bring them up unless appropriate to the conversation. They also tend to more open with those who had the same experiences. As a peacetime Marine, I have always felt a little to the outside. Especially around those marines who fought in WWII, Korea, and Vietnam. I would never presuppose to wear something I didn't earn.
Incidentally, some vets who are real vets have poor memories, so we should take care not to think they're phonies too. For example my dad was an RAF mechanic all through WW2, but as he got older he regularly began mis-identifying aircraft on TV; for example "That's a Mitchell Marauder" he said once, whereas in fact no such aircraft existed..
And in books too, genuine vets occasionally make mistakes, so there again we shouldn't automatically think they're phonies, it could just be their memory playing up