Why do HH ask for staffer contact?

At least in my group, a few of the recruiters called our staffer to run reference checks. YMMV as my group was quite open about PE recruiting. 

Del

They generally know which groups are open about recruiting. If you don't want your group to know you're looking, say that and don't give a staffer name. But the reality is that unless your group is one of the few super anti-recruiting ones, someone will give staffer name and the staffer will give HH the lowdown on all the analysts 

I'm a MM where there's has been limited buyside gig and recruiting is definitely not well accepted. Should I avoid providing the HH with reference or contact to staffer?

Personally would just specify “please do not contact without permission” whenever I provided staffer name. Just did on-cycle and no one contacted staffer or even asked. If a HH had asked I would’ve said only contact if an offer was contingent on it, but otherwise not to

the HH all call your staffer and get run down on each of the analysts in the group, if you don't put him / her down, someone else probably will.