I've never heard a rule, but my interpretation is that it means many, so you'd use the plural form of the verb.

I would interpret it this way:

[20 percent of] Americans live...
[one fifth of all] Americans live...
[one in five] Americans live...

Thank you!

Sounds good to me. That's what I told my
students but they want a RULE.

There's a discussion in the Cambridge Guide to English Usage (covering AE too):

Opinion and usage is generally in favour of plural; however if the individual writer is conceiving of the "one" as singular, it's completely acceptable to use grammatically singular forms.

I have an afterthought...

One might in fact say "one American in five lives in a city". One wouldn't say "one American in five live ..."

And (contrary to my original advice), it would also be possible to say "one in five Americans lives in a city", which would give the sentence a slightly different emphasis than "one in five Americans live..."

The point is that "one in five Americans" does not mean quite the same thing as "20 percent of Americans". Mathematically it's the same, of course, but the image that it brings to mind is different: with this wording ("one in five") one might in fact think of five Americans rather than 60 million (= 20% of 300 million). "One in five Americans live in a city" tends to emphasize the meaning of "20 percent of Americans", while "one in five Americans lives in a city" tends to emphasize "one American in five".

I still prefer "one in five Americans live", but as I think it through more carefully, I can see that it's not quite as straightforward as I first thought.