True. This is why that unfortunate moniker "aquatic" is misleading.
And on your second point: warm water protects from cold, and even from venom if local venomous animals can't swim. And there is plenty of naturally warm water around. Regarding the other reasons to lose fur, I'm still waiting to see any other animal which has lost its fur for any of the reasons above. And yes, the world ran out of water; specifically, the immediate habitat of our ancestors at one point ran out of warm water.
You have to keep in mind that it has been scientifically proven that the modern humans had a few very close calls in their history, and that we are descended from a small group that at one point had no more than about 1000 individuals, who probably inhabited a small area. So all the effects could have easily be local to produce the modern traits.
That's not disputed. There's food in them shallow pools and there's plentiful evidence of people eating tons of shellfish etc, all around the world. This is also indisputably NOT an aquatic ape. The swimming macaques in the Ganges delta aren't aquatic apes. They are land monkeys who can and do swim and search for food under water. Tigers swim, they are not aquatic cats. Elephants can swim for miles, and lots and lots of other land animals can and do swim a lot. But that still leaves them far, far short of being aquatic animals.
The reason is almost certainly that their environment has somehow provided them with equivalent protection
Really? Fur protects us from cold and venom but water replaces that protection? There's no other reason to lose the fur? Like parasites, and a tropical climate, and animal skins a.k.a. clothing? Oh wait, you say that clothing came after we lost the protection of water, because the world ran out of water?
Yes next time I jump in the pool and feel the cold water, I'll think boy I sure with I was fury like an otter.