I think one of the strongest messages from this though is that you should take your kids to lessons such that they can be reasonable swimmers. I had lessons from a very young age so although mum still watched like a hawk there was some confidence there.
My kids are strong swimmers - my parents live on a lake so we started swim lessons at two. That still doesn't raise me to the comfort level of having kids in that 'in between' age here unless I'm willing to trail them. Say six to ten or so.
Home for us is BWV. Starting around five, the kids could get in the pool themselves. (Before that, I pretty much had to be in the water with them - too deep and they lacked the common sense to keep enough energy to be able to swim back if they got out too far). I'd have a swimsuit on, and a book, and get a drink from the pool bar, and look up and be able to spot them. Or sit and chat with my husband. That sort of half an eye on the kids thing you do when they are that age. If you want to let your kids go free range, but you still want to be able to look up and spot check, SAB isn't a good pool - regardless of how strong they swim. Also, its pretty easy to get lost at SAB if you don't know it. Its easy to get a little turned around in there - and for pre-tweens, they could just have a hard time finding you and panic.
My kids are now ten and eleven, and now I don't have an issue with it.