Yes, I guess there are those who, when they play cover songs, try to play them note for note. It's almost like there is a "score," and you are being faithful to it. And then the joy of listening, would be that the audience hears exactly what they expect to hear, when they hear it.
This seems so pointless to me. Like working a crossword puzzle. Everything neat and in it's place.
If you are going for a "note for note" experience, hell, why not just listen to the original? I have always approached cover songs as "raw material," a starting point, subject to interpretation. If a song is really, really good, it will hold up, and then the joy of listening would be to hear the song in a new way. Maybe a big production number would sound new and refreshing in a stripped down mode? Or maybe it's the other way around?
Anyway, yesterday we ran through a bunch of cool cover songs with our band. And we did make the songs sound like our songs. That's the way to do it!