Wait a sec. I re-read the OP and i think what she's saying is that her partner didn't tell HER the whole truth ABOUT telling the girlfriend. I thought the OP was worried about whether he lied TO the GF about not telling the gf about the "3 rule". Still, it sounds like it's a red-herring for some other issue, and this whole business with micromanaging other people's relationships means that some other issue or dynamic is needing to be dealt with.
Now if that is so, a lot of the stuff i said earlier doesn't really apply to your situation. It does, but not as to your question.