Nonsense. I learned to do it long after I was 3.

This might help: put your tongue (but not the tip) just above your teeth, let it relax, then blow air out so your tongue flutters.

stick the tip of my tongue to the roof of my mouth

If I do that, it gets stuck. What I think you want is the hard palate (behind the teeth), not the top of the mouth, and keep it relaxed.

I guess I should add that I'm neither a native speaker (though I've studied more than one language with rolled r's) nor have I any experience teaching this skill. I'd bet money you can learn it, though.

Edit: one more thing - you may find it easier to try words that end in a rolled r. The words that begin with a rolled r are a little harder (to me).

And in any event, that wouldn't mean there are words in Spanish with rolled final r's, which is what was being discussed, just that people might pronounce a word that way.

Radio is "Rradio".

I've found amusing how some people who learn english as a second language end up pronouncing spanish as "espanish", since no spanish word begis with s(consonant), except for sh.