New Line bought not only the franchise but also the title Friday the 13th a while ago I believe. So there isn't much of that sort of an issue I think but its possible Paramount might still own a small part of the first film, just enough to make New Line have to bring them on.
Dunno why, apparently Paramount really doesn't like the series for being so successful and being in the horror genre.
Last I heard Platnium Dunes (Bay's company), New Line, MTV (up in the air at the moment), and possibly Paramount are all gonna get behind whatever they wanna call their remake. Dunes I think will be the production company as thats what they have done with all their films, make them then sell them to a studio for distribution.