I think you're referring to deionized water. Deionized (DI) water is water that where all ions are removed. This is not safe to drink.

Distilled water is boiled and recondensed water, which leaves you with pure H2O (no minerals etc). It's safe to drink but pretty bland.

Outside of hydroxide and hydronium, which ions are left with “pure H2O (no minerals etc)”?

And DI water gets hydronium and hydroxide pretty quickly (if they ever go away.) H2O just breaks down into OH- and H3O+ on its own (as far as I know)

I agree: in fact the deionization process adds one hydronium or hydroxide for every (mineral) ion it removes:

>Deionization is a chemical process that uses specially manufactured ion-exchange resins, which exchange hydrogen and hydroxide ions for dissolved minerals

https://en.wikipedia.org/wiki/Purified_water#Deionization

In other words, if deionized water is unhealthful because of a lack of ions, distilled water is, too, because it doesn't contain any more ions than deionized water does.

What's their take on reverse osmosis?

"RODI" (de-ionized reverse osmosis) water can be as pure as distilled water, and is common in labs. I'm told you don't want to drink the lab-grade stuff.

Reverse osmosis devices include mineralization filters, which add salts to nearly-distilled water.