Listen to any number of live albums from any rock band and you'll hear lots of deviations from the studio versions.
I learn from the version that is most familiar to my target audience, and that's always going to be the most popular hit recorded version that got played and heard the most.
You go ahead and learn from whatever Live at the Whiskey A Go Go 1983 version you feel like, that's your prerogative.
I know which version gets me gigs, cash, and repeat invitations.
What the original band does to their music live on stage is of no use to me, because it ain't about me, and my audience has little to no interest in or appreciation for re-mixes and live versions. They want the Big Mac the way they've had it a million times before.
Sometimes the original act does all nature of things to their music on stage, tempo changes, key changes, re-writes, totally re-worked arrangements. Having created the original version, they have that option and can approach their ticket-buying audience however they please.
I'm not rolling the dice like that with my target audience. We'll take liberties with intros and outros, and occasionally add an extra verse/chorus or solo to short songs. Once in awhile we do a segue or beat-matched medley. In my area, mashups are very hit or miss, usually miss, so we avoid them. The "creativity" is in the presentation, aesthetics, and audience interaction. Otherwise, the main body of our covers are very faithful and instantly recognizable, with details and sweeteners to match the most popular recorded version.