I'm basing the following on a sample size of one — myself, but I imagine it's true of most people with good musical ears... it's interesting that hearing non-pitched sound at the beginning of a song you know well — drums, a count-off, sound effects, or even talking — is enough to cue you to the key, the starting pitch.

I've also noticed that when thinking of a very familiar song, like a Beatles song, I remember it in tune. I don't have perfect pitch, but I can often do this.