As with many things music, it is a subjective issue I think. To cop the feel of a piece is how I generally work, especially when depping or busking a tune without rehearsal or prior learning. Other situations require absolute detail to a written score - although sometimes you have some 'artistic licence' provided you spot the unison parts!
And there are situations where I feel blasphemous to even dare deviate from the original line because its so good.
I don't know how others feel, but some lines (a few notable ones include Good Times, Addicted to Love and, oh loads really!) have a subtlelty within in that on the surface they are fairly straightforward, but to get CLOSE to the original requires a lot of attention to beat placement, tone, articulation et cetera - some players deviate by adding fills and skips and so forth but it does not necessarily enhance the groove it sometimes distracts and also highlights how a fill without reason can be a way of disguising a lack of focus on the groove - the tunes mentioned are so well played they don't need lots of fills/variants.
Bit of a can of worms as always this, but one way to know for sure is to record and listen back.
That said, play to a load of pissed people and they probably won't know/care. As long as you play Kings of Leon!