I don't think a covers band is obliged to try to replicate a song at all. I love putting your own spin on a song. For example, a band I used to play in did our own version of 'Come Together' by the Beatles. It was quite a heavy sounding band, and when the singer announced the song there would be a bit of a groan from the audience. They soon shut up when we launched into it in a drop D tuning. Sounded wicked and we used to get asked to play it over and over.