UW Whitewater , which won the DIII championship in May, had about 100 players try out for the team this fall. Success does that!
The real question is, how many were recruited? Most if not all DIII schools hold open tryouts. So anyone who decides to attend school there can tryout.
The School my son is attending has something like 20 freshman trying out. Again the question is how many were recruited and how many are just trying out to see if they can make it.
In addition, as you alluded to, since the school does not get a letter of intent from their recruits they may also recruit more aggressively because they really do not know who will actually show up until September when classes start.