I almost always use first-person view playing Morrowind. When talking to the gods for the Daedric shrine quests, I've assumed that my character was hearing a disembodied or telepathic voice when the gods spoke.
I just activated Sheogorath's statue in his shrine below the St Delyn canton. He gives a long speil about the Fork of Horripilation and Sheogorad and blah blah blah.
Anyway, the game went into third-person view during Sheogorath's speech and I saw that my character was doing the talking! I never saw my player character doing a speaking animation before. It was like the god was taking control of my character's own voice to give him the quest.
I went through the start of this shrine quest again with a saved game. My character gave Sheogorath's whole speech!
Does this happen on the other shrine quests? Maybe i just missed it until now? LOL

I think it probably happens with all of them. ^^ It took me a lot of playthroughs to notice it as well. I don't know if it's a side effect of the engine or if it was intentional. Either way it's kinda spiffy.

Wow, that's freaky...

One would presume that the Daedroth Prince in question would temporarily use your body as a vessel to get his message across, though I always thought that they spoke into your mind.

I've seen the same thing happen when Lilarcor's speaking. It's probably a side-effect of the PlaySound command; the mouth animations act as a sort of "visualisation". Either that or the scripts use the Say commend instead!

It's probably the only way the morrowind engine can do it. maybe someone could make a talking shrine mod with animations for the statues.