Someone might ask, "Well, Mr Bruce, all you have to do is ask them what's going on, and I'm sure they'll be happy to explain it to you, if it's all that hard for you to figure out." The Trinity Pro-Cathedral e-mail is out of order. There is no e-mail listed for "Bishop" (or is it "Pastor"?) Williams. St Mary of the Angels answers neither its phone nor its web contact. The press information officer of the ACA Diocese of the Northeast, a Ms Bonnie Turner, does not reply to requests for staple information, such as the ACA's policy on background checks for priests.
I doubt if there's actually much thought behind this. I can only assume the ACA recognizes at some level that neither Williams nor Rivers has been called by an elected vestry, so neither is correctly styled a Rector (upper case R). This is a tacit acknowledgement that there is in fact no elected vestry in charge of St Mary of the Angels, so they are sorta-kinda inventing a whole new hierarchy, but not exactly. By the same token, Williams is still a Rector (upper case R) back in New Hampshire, so he has something to fall back on when the ACA's legal case finally collapses, and it will make it more difficult to serve him with papers back there when the time comes.
I saw a true crime show on TV the other night where this bigamist had a wife in California and a wife in Florida and had to make up a convincing story that would keep both of them in the dark about what was going on. Seems like something a little like that is going on here.