I think I just figured it out. At timecode 0:55 - 0:57 Brian Jones appears to be playing an F then an E (on an alto recorder) and the sound that is heard is, indeed, an F then an E.
But if that's the case, I'm still confused at the fingering observation that I made in my post above; the sounds that are heard in both instances are the very same F, yet the one at 2:31 does not appear to be fingering for an F.