~てもいい is a fixed expression for permission. も doesn't have to be there, but usually is. I believe the implication is normally してもしなくてもいい, but that seems a bit strange in this case. It could just be that it had more of that sense before, but it's just been used in that form so often that the effect も has has lessened. Or there could be some other explanation, but either way, ~てもいい is used all the time for expressing permission.