Right, I agree with all that, and I agree that the preposition "de" should be included. I was getting too much in the linguistics of the term grammaticality. For anyone who cares on the subject, go to the following link:
http://www.ling.udel.edu/eastwick/li...de_vs_pre.html
It discusses descriptive vs prescriptive grammar. Since grammaticality is defined by the native speakers of the language, technically saying "darse cuenta que" is grammatical, because native speakers of the language use it, and it
is understood. This is an example of
descriptive grammar. It is not taking any side, it is simply saying that it is used by natives.
Prescriptive grammar, on the other hand, is what you both are referring to, "darse cuenta"
should be used with "de." It is like a prescription, some native speakers say that's how it should be.
We have tons of cases of prescriptive vs descriptive grammar in English, as well (if you follow the attached link, you will see more examples).
For example, descriptive grammar would simply say "prepositions are commonly used at the end of a sentence in English"
I.E. Where are you
at?
On the contrary, presciptive grammar would say "prepositions are not supposed to be used at the end of a sentence.
I.E. Where are you at?
Where are you?
There are tons of other examples of this, for example saying:
"Me and her went to the store" instead of...
"She and I went to the store" (prescriptive grammar and how it "should" be)
If this is over your heads, I apologize. I am just trying to understand the term grammaticality as it is defined linguistically, and how it is further broken down into descriptive and prescriptive. Thus, the term "grammatically correct" and its variants, is much more profound than anyone who hasn't studied linguistics would suspect.