Shania's "Any Man of Mine" actually does sound country and is played (or was, since I haven't heard it lately) on one classic country station I listen to. But not long after that, she started doing crossover stuff that I really hope doesn't show up on the good stations. That's not to say all of her music was bad, but she's one of the offenders.
"No One Needs To Know" was easily her most country-sounding single, lots of steel guitar and the percussion is understated to the point of not being noticed. It would have been a country hit in the '70s with no problem at all.