Average the tempo including all fluctuations to get a clearer idea in my opinion. Chances are the band swims as much as 10 BPM or so throughout the course of a single performance*. When you take those 10 BPM into consideration, even the fastest tempo is not radically different than the recording.
“Steady state” tempo is a much more solid indicator of how fast a band plays a song than an isolated 15 seconds in much the same way that the “steady state” note content of a vibrating string is a more solid indicator of being in tune than isolating a tiny fragment of the wave form of somebody plucking a guitar string and letting ring out as a note. This is because the note will tend to go pretty substantially sharp immediately after its attack before momentarily easing into the “steady state” note and then shortly thereafter going all kinds of haywire as the fundamental frequency gets overshadowed by overtones.
As a bonus aside: tempo and pitch are both measured in BPM. For example, 120 BPM is a nice medium tempo for pop but 26,400 BPM is the note A above middle C. For a fun time you can easily test this comcept: load a kick drum sample into a DAW at 120 BPM and speed it up to a tempo of 26,400 BPM. It will sound exactly like A!!! (How I arrived at this crazy tempo: A=440hz which is 440 beats per second. 440 beats per second x 60=26,400 BPM lol. It works.)
Long story short, there are parallels to be drawn here between the speeding up and slowing down of tempos and the in tune-ness/out of tune-ness of a plucked guitarist string: both ought be measured in terms of their average BPM as perceived by human ears as opposed to absolute BPM measured in an isolated bit.
*Btw most every band on earth is gonna swim 10 BPM or so playing arena rock in actual arenas. So no knock on the Pumpkins.
More fun:
https://youtu.be/_gCJHNBEdoc