My late grandfather was also in that record crowd for the Stoke game in 1934. He also always insisted it was significantly bigger than the officially stated figure of 84,000-odd.
As for Peter Swales, when I started going to Maine Road in the mid-seventies. I remember they always used to announce the crowd over the tannoy in the second half, and it was far from uncommon for it to seem so outlandishly understated that people all around you would laugh at it. Roy Bailey, the ex-physio, posted on Twitter a few months ago that, in those days, the players were on a crowd bonus whenever gates topped 33,000 and as a result Swales would quite commonly have the attendance declared to be a suspiciously low figure just a bit below that.