I agree that Queen played ABTD in the key of E, not F. Two vids are below. The first one is a live vid. I can clearly see Deaky playing it in E. The second vid is the studio version. I can also see Deaky playing it in E, but if you compare the pitch of those two vids, the second (studio) vid's E is at a slightly higher frequency. So yeah, I think they "sped up" the studio version. But most definitely, John is playing the song with the low note as an open E string.
Live vid:
Studio vid:
Live vid:
Studio vid: