It all started last year, when CDMsports.com sued Major League Baseball because MLB had threatened CDMsports.com for violating players' right-of-publicity by exploiting stats that belong to MLB. They argued that a players stats received more publicity than their faces, so their stats were protectable.
Of course, this position sports (pardon the pun) lots of First Amendment issues. CDMsports.com argued that newspapers regularly republished this information, and MLB (whom, like CDMsports.com, runs a fantasy-sports-league) was merely targeting a competitor.
CDMsports.com won the lawsuit, with Judge Mary Ann Medler ruling that the First Amendment trumps right-of-publicity laws. Predictably, MLB appealed the ruling, arguing that reprinting stats is the same as taking someone's picture and putting it on posters and coffee mugs.
There is a major problem with that argument. Everyone who would want to participate in a Fantasy Sports League already knows the names of the players, as Judge Morris Arnold points out. CDM has built their business not on using players as publicity, but on providing a valuable service based on public information.