We just got back from St. John, our 4th trip in 4 years. I've never heard anything about not being allowed to shore dive there, but it's just not something that you see much of. The snorkeling is so easy and so good in almost all of the bays that there's really no need to gear up for scuba. Seriously, we've seen loads of underwater life snorkeling there -- sharks, barracudas, squid, stingrays, eagle rays, turtles, octopus -- it really is quite good.
Nearly all of the bays require some amount of hiking to get to the shore, so that may be one reason there's not much shore diving... it's just cumbersome to schlep the gear along. A buddy of mine has done some shore diving down at Hart Bay, on the SE part of the island, and he says that is a good dive site, about 50' depth or so.
As far as boat operators, there aren't many options -- on the west end of the island, Low Key Watersports goes out of Cruz Bay; Cruz Bay Watersports goes from the Westin dock; and Paradise Watersports goes out from Caneel Resort.
I assume the "Brad" you were referring to is one of the owners of St. John Dive Adventures out of Coral Bay -- we dove with him a couple days last week and had an incredible time. Brad & Jay's boat takes a maximum 6 divers, and the sites we went to were spectacular. Brad is a wonderful guide, and I would recommend this operation in a heartbeat.
Angie