I'd go under the drywall for a look. If it's been going on for awhile
the subfloor may be trashed.
We had a similiar problem at our place. A bad original plumbing job
had the drain at an angle coming up to the floor and half the flange
unsupported by wood (the gomer used a hole saw and cut a cloverleaf
shape too big for the flange so part of it was just floating).
Eventually the seal broke from the wobbly installation, flange rusted,
leaked into the subfloor, and made a hell of a mess.
We had to cut out a chunk of the floor and replace it, sister the
joists under it and replumb the drain with a new flange.
If you don't fix it right the whole mess may not be stable and the seal
won't hold. If it's bad enough the toilet could come through the floor.
Since you have to patch the wet drywall anyway I'd take a look under it
to see what's going on.