References being taken depend on various factors. Like time of the month, who is PO doing screening, etc etc.
Im a big believer in power to the people and lots of public info, but since orgs read these boards, saying who can screen loosely may result in making those orgs reconsider.
I'd say, there are three main tiers. There is loose screening that most orgs don't accept, there is good screening with ref sharing, there is no ref accepted. All orgs know each other's phone #s and they all know who screens or who don't. And many have a phone db of mongers they share. Kind of a review cache for mongers.
Corgs are usually solid for stepping stones too. Unlike korgs where korgs can say they don't reply, corgs will reply to ref checks.