I agree with both point of view.
It should be flexible.
Many tunes can be played, re-arranged, re-harmonized hundred ways (especially in jazz)
That can also be applied for some pop-rock songs as well. But in my experience, when someone request a song for such genre, they usually expect the original recorded version. The variations may comes from the singer's performance of the song (phrasing, feel, voice tone, etc) rather than change in harmony or tempo and groove.
Tempo change can be an issue for vocal based music (because some words can be difficult to understand at higher tempo, not to mention breathing limitations). It all depends of the song.
A good practice is to have both (original arrangement of the tune, tempo, structure, harmony and also re-arranged versions when suggested (and arranged) by band members.
Unless specified otherwise, I usually go for the original version