For what it’s worth, I did just test it with airplane mode and it still correctly identified the song playing. So at the very least, it’s not lying about using a local database to identify songs, at least when it is offline.
It also uses a cloud fingerprint database apparently according to the second paragraph:
If you turn on “Show search button on lock screen”, each time you tap to search Google receives a short, digital audio fingerprint to identify what’s playing.
Oh, I didn’t notice this, my apologies. Turning on identify songs nearby reveals two new options, notifications and show search button. That show search button option must be new; I had identify nearby music on already since my last phone. Guess they added something new. My bad.