Same here. When I ask my friends who are not musicians and casual music fans about this, they always respond that they want to hear something really close to the original.
My current band does the "lets do the songs OUR WAY" thing, which pretty much translates into: "I figured it out just enough to get through it and dont want to bother learning any details so Ill call it 'doing it MY WAY' but it really means I couldnt be bothered". And if I say anything they say "people would just turn on the radio if they wanted to hear the song the original way" or "we are not a tribute band".
I believe you have to look at each song and determine what details NEED to be there and then do it. No, I dont play every song note for note exactly like the original, especially when its a boring, repetitive part. I will embellish. But I analyze each song and figure out what details have to be there. Things have gotten better over time in my band, but there was a time I thought about leaving over this issue. Im not against adding something to the songs, but only if what makes that song identifiable is already there.