I agree that the song is automatically connected to America because it refers to the Rio Grande.

But I think there's more to the song than just the connection to America. These are very suggestive lyrics, filled with double entendres; comparing a woman's body to the landscape. This metaphor is made even more directly the first time the words "Her name is Rio" appear.

The implication is that the action of the Rio Grande through the "sand" creates canyon gaps that are suggestive of a vulva. "Cherry ice cream smile" refers ostensibly to a woman's lips, but a woman has two sets of lips, doesn't she?

The hint of a woman's breasts and their sexual connection to the vulva is made in this line:
"From mountains in the north down to the Rio Grande"

In the following line, the woman dances provocatively so that a glimpse is caught in the mirror
"With a step to your left and a flick to the right, you catch that mirror way out west"

This line is very directly about a woman who is exposing herself
"And when she shines, she really shows you all she can"

And the voyeur is enjoying it
"Like a birthday or a pretty view"

Here the lyrics refer to the various places where the voyeur has gotten a "pretty view"
"I've seen you on the beach and I've seen you on TV"

And finally, the voyeur has an encounter with "Rio" but they get in trouble for being exposed in a public place
"At the end of the drive, the lawmen arrive"

But the voyeur doesn't want to stop
"You make me feel alive, alive, alive,
I'll take my chance, 'cause luck is on my side"