I'd bet good money on if you called yourself a policeman or military personnel of standing you'd be breaking more serious laws than that of a civil fine.
I can call myself a police officer or even a four star general. It's only once I try to take actions as such that laws come into effect. The Supreme Court recently overturned a law that penalized someone for claiming to be a veteran. You are free to claim to be active duty or retired military, regardless if it is true or not, so long as you do not use this as a ruse to collect benefits (monetary, access to facilities, charity, etc.). It is only after the speech turns to actions that the free speech protections provided by the Constitution cease.
I think that you are probably referring to the Stolen Valor Act of 2005
https://en.wikipedia.org/wiki/Stolen_Valor_Act_of_2005 and you are absolutely right that the SCOTUS found it to be unconstitutional in 2012. It is an interesting story I think because it illustrates the evolution of the right idea ( prevent people from falsely claiming to have earned the medal in an attempt to protect the valor of legitimate recipients) to conform to accepted principles (freedom of speech).
In response, two things happened that were worthy of note. 1) A publicly accessible registry of award recipients was instituted
https://valor.defense.gov/ although it is currently somewhat limited. 2) The Stolen Valor Act of 2013 was passed into law
https://en.wikipedia.org/wiki/Stolen_Valor_Act_of_2013. That law, which is in effect today, addressed the intent (i.e., "do not use this as a ruse to collect benefits", as you have said) without the infringement on Freedom of Speech.
If I recall from my reading (just now) one of the Justices said basically (re:2005 act) - what's next, imprisonment for lying about your age? (well, it was said with a bit more gravitas
)
I am filling in some of the details (not even mentioning the lower court decisions) because I think the process (come out with it - test it - revise it or dump it and figure out another way) is relevant to the original topic. Hopefully, the evolution will be a little quicker.