"Fake it 'til you make it" is more about pretending to have confidence before you really have it and less about falsifying your past in a way that's easy for someone to fact check.
Correct. I'm familiar with the trajectory of the "Fake it 'till you make it" meme, but I have never understood it to be a PC synonym for fraud, or passing yourself off as something that you are not (including missing payroll and falsifying investor interest or mundane things like your C.V.)
Early in my career I was a bit gray on some skills. For instance, I may have done some tutorials on ActiveX and oversold my knowledge, but by the time I started the job, I put in the work to ensure I could back up my BS.
[0] http://www.wired.com/2013/04/fakeit/