I want to be careful about playing guessing games, but there is a pattern I see often among my Swedish ancestors. I wonder if something like it might be at work here. Dedham society would have been very different than Swedish society, but one thing that would be the same is the centrality of the church and minister in local affairs.
Young woman works as a maid at the vicarage, the only servant of the minister and his wife. Her parentage never seems to be clear. Probably she is an orphan. She marries a local farmhand. The wedding takes place at the vicarage, reinforcing the impression that the bride has no other home, or at least no local family.
The groom is very often from a poor, local family, either an orphan himself or son of a widowed mother. Through the good offices of one of the local landowners, they become tenants at one of the local crofts almost immediately, which suggests that the timing of the marriage has been arranged to coincide exactly with filling the vacancy there.
This is very close to the scenario Erica has outlined for John Rice, where the Allins and local opinion might have matched John and Ann as being suitable for each because their station in life and future expectations were approximately similar.
In the cases I'm describing I always imagine, maybe somewhat fancifully, that the groom is probably a "good boy", a bit on the religious side compared to his peers, perhaps having a pious mother, and perhaps looking up to the minister as a father figure more than other young men his age.
And I imagine the young woman as being herself more than usually pious, from her teenage years of working at the vicarage if not otherwise.
In two cases where family tradition tells me something about the people behind the names and dates, I know that the young men wanted to be ministers but their families couldn't afford the education.
This is somewhat the way I picture John Rice and Ann Hackley. I want to caution, however, that this is just an exercise in imagination about what could have happened. I would be very distressed if someone comes back later to say that I said John Rice wanted to be a minister or that Ann Hackley was a servant of the Allins ;)