Plenty musicians can and have recorded music without knowing music theory. You don't need to know what a Dsus4 chord is in order to walk up to a piano and hit the D-G-A keys. There's "knowing what a chord is" as in being aware that multiple notes simultaneously played "is a chord," and then there's "knowing what a chord is" as in picking out the chord tones and its inversions when a chord comes up in a piece of sheet music. Virtually everyone knows the former, but it's very plausible to be a recording musician who can't do the latter.
Michael Jackson didn't know music theory in that way either, but he obviously made a song or two in his day. The same goes for Dave Brubeck, Stevie Wonder, and the Beatles. None of them "know music theory" in that sense. It's wholly plausible Adam could fall in a similar camp (although his music is hardly of that caliber).