Yes they have MLB exclusive rights.
No, 2k7 does not have exclusive rights to MLB. Thats why there is MLB 07 the show. So far the consensus is in and MLB07 has the better reviews. I had MLB06 and just picked up my copy of 07, can't wait for the roster update.
http://www.gamespot.com/ps2/sports/mlb07theshow/index.html
http://www.gamespot.com/ps2/sports/majorleaguebaseball2k7/index.html