That's why we beg recruits to come here? Because it's a privilege? For us, or for them?
Tyrann Mathieu had one BCS school scholarship offer - LSU. Nobody was begging TM to go to their school (well, maybe FIU, Tulane or Southern Methodist...a few of the other giants that recruited him). Frank Wilson, who recruited him at LSU, couldn't even get Tennessee to look at him because of his size before Wilson left Tennessee. And we know what state Tennessee's football program has been in recently.
So in Mathieu's case, it was an absolute privlege to play in Tiger Stadium because no one else was knocking down his door. He was only a 3-star recruit and everybody felt he was too small. LSU usually goes after the perceived cream of the crop.
It's even a privilege for the top recruits. Yes, LSU obviously benefits too, but you never know how someone will pan out. Sometimes you can be great and still get passed over on a scholarship offer because a coach has other needs or doesn't evaluate you properly.