Yes, that is a huge generalization... INDEED!
When I lived in PR, I didn't pay much attention to the way folks communicated, that is, beyond the obvious differences when compared to my country of origin. I did notice, however, that some folks pronounced the double-Rs, as in 'carro' or initial R, as in 'rodilla' with a certain throaty sound. It was most evident with people from the interior, whom some consider jíbaros, or country folks.
While living in NYC, I started paying attention to PR news, and I was extremely impressed with the way PR politicians communicated.
As an interpreter in the Dallas area, I can say that I've witnessed proper Spanish from all nationalities, yes, including Dominicans, Cubans, and PR folks.
But I've also had to interpret for Mexicans, and Central- and South-Americans whom did not communicate as well as others. So, I'm with you, Marianopolita, and believe that we should not generalize so readily.
I'd venture to say that most of us can shorten a word with full knowledge of the proper way:
Ya 'tamo cansao de e'ta lluvia vs "Ya estamos cansados de esta lluvia".
¿Pande tú va? vs ¿Para dónde vas?
¿Cómo tú 'tá? vs ¿Cómo estás?