Gwern is apparently familiar with more quoting styles than I, because no style I'm familiar with allows quote marks of any kind for something that isn't a direct quote.

Don't single quotes normally indicate paraphrasing?

No. Quotes, single or double, normally indicate quotation, or a few other things such as the use-mention distinction, but never paraphrasing.

Under some quoting styles, yes, they do. But no quoting style is so prevalent that this alone decides the question.

I was taught that single quotes are nested inside double quotes and vice versa, the default being double, but that they're otherwise equivalent.

Maybe you're thinking of scare quotes or glosses, but they're normally restricted to single words or short phrases.