The dorade boxes on the Hunter 37 were pretty poorly made. The part you see on the outside is cast with the deck. Inside, you see the part that is part of the liner, which consists of the top of the cabin and the two openings which extend upwards into the box.
What you don't see is the problem. If you remove the teak covers, you'll see that they sealed the bottom of the opening with a piece of plywood. If it wasn't there, it would open directly into the cavity between the liner and deck, allowing water to migrate all through the boat. In fact, the way it was done, on some boats, this is exactly what happens.
They simply put a piece of plywood with champfered edges in before the liner was added. Then a bit of chopper glass was splattered on it. On mine at least, it didn't seal it up. Even if it sealed most of it, the liner was added afterwards, which meant the round protrusion that lets air into the head didn't get sealed.
I've talked to a number of owners who claim there isn't a problem on their boats, and in fact, some may have been done better than others. There is an easy way to tell.
There is a small opening on the side of the box on the outside. This is where water normally would leave the box. Tape it shut so no water could escape. Then fill the inside so that water is filled up to the lip of the hole that lets air into the head. you can feel this from inside the boat by curling a finger up and over the lip when standing in the head. Let it sit for a time, overnight would be good. If no water disappears, you don't have a problem. If it does, it went between the liner and deck.
This is a real problem. It will rot the core, it will drip into various areas ruining many things below and rotting the coring of the deck.
The fix is pretty simple once you've identified the problem. Remove the teak covers on the boxes. To do this first sand the varnish off where the round plugs cover the screws. This will let you get the plugs out with less damage. Then drill a small hole in the center of the plugs. Take a small screwdriver and pry out the plugs. If you don't remove the varnish first, you will probably break away some of the teak around the plugs. Then simply unscrew the screws holding down the the covers.
Now, for the repair, take a sharp wood chisel and chisel out all the wood that is sealing (well, sort of) the bottom of the box. Once that is done, it's a matter of fiberglassing the bottom solid. Make sure it's completely sealed. Then reinstall the teak cover, put in new teak plugs, sand them smooth, re-varnish.