I haven't tested this, but if I had to guess... The river v. pond problem may have to do with the same traversability rules that apply elsewhere.
An animal has to be able to turn around a full 360 degrees in a space in order for their hitbox to count something as traversible. So crocodiles can't go through a passage that is large enough to fit their width (going in heads first, like they'd do in real life) unless it is also long enough to fit their length (walking sideways somehow). And sometimes it's more 360 degrees horizontally and vertically (so a giraffe, for example, might need enough space for the to lie down head to toe, not just enough to walk through the way they normally would).
Again, I haven't tested this fully, but my instinct is that if the deep part of the river was wide enough for the animal to go through at any 360 angle (swimming forward or swimming sideways), both horizontally and vertically, then it might count. But if they can't turn around 360 degrees in every 3-dimensional direction and still be within the 4 meter deep area at all times, then it won't.
This would also explain why you can't test the amount of deep water before placing an animal. Since different animals are different sizes (caimans v.s crocs, for example), the amount of space that is going to end up "counting" as deep water depends on how that particular animal can traverse it. It might also explain why going deeper doesn't help, if the original width of the rive isn't sufficient for them to twirl around in to begin with.
Again, this is just my hypothesis based on what I've read here and what I've seen elsewhere in the game.