I do find it a little odd that parents would permit their sons to live in a fraternity house but not to actually join the fraternity. Are they worried about hazing? (Most GLOs have anti-hazing policies these days.) The expense? (Do what many of us do/did... get a part-time job.) The parties and alcohol? (You have access to parties and alcohol whether you're greek or not.)
As for not having a full house - my school recently implemented a change in policy. Formerly, all fraternity members including freshmen/pledges had to live in their fraternity houses. Starting this year, freshmen can pledge, but all freshmen must live in the dorms. This has left a lot of fraternities with empty beds. Some fraternities are housing what you call randoms - usually grad students, since grad housing is very scarce. Others are just eating the cost of not having a full house. Those that are housing randoms are just doing what they have to in order to hang onto their house until they either (hopefully) rush in some large pledge classes and fill the house again, or have to give up the house.
And housing independents isn't necessarily a bad way to meet some potential brothers and show them firsthand what your fraternity is like when it's not rush week
