Proof that Water Pets are supposed to have significantly increased health regen:

[Theturtlehermit]

iirc , water pets had a flat +15 or so hp regen per tick at lvl 4 and this remained until higher levels (50+, perhaps) where the numbers for all the elementals change in calculus abit. Still, the water pet always outshined the other pets for health regen by far. And without commanding the pet to sit, which gave it additional hp regen if you did so. (cant remember if the sitting mechanic was classic or not, but i think so)