I've played tennis once in my Frees, and it was a bit different. I'm not a regular tennis player, so it's always a bit odd anyway though.
My thinking is that many tennis players would say that because they are acclimated to having all that support in their traditional shoes that their feet/ankles NEED it constantly. It would probably take some time to shift from that to a more minimalist shoe, but I don't see why it would be a problem as long as your feet have adjusted themselves so that the support is coming from the underlying muscles/tendons/etc. rather than the shoe.
Not an overnight switch, but long-term I wouldn't see why it's not possible.