My take on covers is that the money on the original has already been made...by the original artist and producers. Everyone can hear that one, nearly any time of day. What they can't hear on that one is the energy of a committed live performance.
One-hundred percent fidelity doesn't necessarily win over audiences, most of whom do not listen that closely. Often it isn't even possible. As someone playing the music of others, our mission is to get to the heart of it without taking large liberties (something that might make the song unrecognizable at first listen), while preserving the spirit of the thing. If the song isn't delivered well, even technical perfection won't get people grooving.
On the other hand, if your groove is strong, booties will shake, regardless of the interpretation.
IME, this works.