Is it a reference to Suetonius' training boys to swim as fish with him?

More or less, though I think Suetonius is just the biographer...

I don't know how that ties to the rest of your post at all or even to the Hillary article.

Well, when a little boy turns to you and says "I'm a fish"...

;)

Some reason why I continue to try to be a good person.

Mostly, because it's good for the bearer. Heaven knows that most everyone else is a servitor of hell, so it's not much for them... it's for you.