Putting the whole chemical leaching issue aside, I'm pretty sure the primary reason for the warning on the Pedialyte bottle is for a completely different reason--bacterial contamination. First of all, these bottles are designed for one-time use, so they aren't designed to be particularly easy to clean. The concern is that bottles which aren't cleaned properly or re-filled with contaminated liquids can harbor bacteria, and we all know that babies and very young children's immune systems are not well developed yet.
The manufacturer's concern is that a parent will think that since they give their child Pedialyte with complete confidence, then the same bottle should be safe to store water or other liquids in, too. Actually, you basically make the same argument in your second paragraph.
The problem is assuming that since the bottle was safe the first time, then it will be safe the second, third, fourth time, etc. The company does not want to be blamed when a consumer reuses the bottle and their child gets sick, even if it's the consumer's fault for not cleaning the bottle properly or re-filling it with contaminated liquid or letting multiple people drink from it and contaminating it that way.
That said, bleach and very hot water are generally not recommended for plastic bottles, particularly bottles made for one-time use. Well, like I said, those bottled aren't particularly easy to clean, like trying to get a bottle brush inside, so bleach may be the only way to reasonably make sure the inside is clean. Use your judgement.