I've had this issue as well. As far as I can tell, it's a graphical thing only, and I've gotten used to it, but it was disconcerting at first.
What happens for me is this: During banning phase, all enemy champs are on display, and those that get banned correctly get the crossed out circle above the icon. Then, when picking phase begins, and the champs switch to only those I own, the circles stay. They move onto some of the champs (usually determined by absolute position they were in, ie. field in the grid, so to speak). The icons are still colored, though, and I can pick the champs. Like I said, just a graphical glitch.