I don't believe it works that way from my experiments in the pool.
For one, when I try it, I don't have water in my throat, the air in my mouth (CO2 and O2) keeps the water out unless I suck water in to displace the air. Even then, it'd just be in my mouth, not my throat.
Also, as it is not just oxygen I'm speaking through, but also exhaled waste gases and other trapped gasses that I inhaled when I began to hold my breath, I don't believe your "more than oxygen necessary for speech" theory to hold true.
When I tried to form words, the sounds were muddled and not understandable by my friend. But then, I didn't have a spell cast on me.
So my guess would be that if I were able to breath liquid I would be able to speak.
Then again look at Abyss. When Ed Harris is in his little emnionic fluid bubble, he doesn't speak, he uses a keyboard. But of course he can hear fine.
But again, he didn't have a spell cast on him. I'd say in the D&D fantasy setting, that Water Breathing allows underwater speech as there really is no other way to do it short of a necklace of adaptation.
If you are suggesting that Alter Self would allow underwater speech, I'd have to say that gills on the exterior of the throat (the popular place to put them in Sci Fi on humanoids), would not affect speech. But I have no idea how creatures such as tritons or merfolk are capable of speech, so maybe a caster familiar with them would simply change his anatomy to fit that.
In any case, I don't think fictional magic requires such a deep level of understanding from us. Suffice it to say, the wizards who invented the spells knew what they were doing and the magic of either spell allows speech underwater when used in this manner.
Or not.

Your viewpoint may differ.