The "de" in "avoir besoin de..."

I'm posting this as a followon to another thread about the use of "du", "de la" and "des". I think part of the confusion that may arise is because of an apparent "exception" with the phrase avoir besoin de.... For example, you get apparent contrasts such as:

  Il me faut du fromage.

  J'ai besoin de fromage.

At first glance, you may wonder why the word for "some" is du in one case and de in the other.

But in fact, in the second case what you have is a combination of the following:

• de functioning as a regular preposition;
• when the preposition is (theoretically) followed du/de la/des, the latter is in fact omitted.

So the second example is implicitly something like:

J''ai besoin de du fromage > J'ai besoin de fromage.

If the second element isn´t "du" (or some other element based on "de"), then it stays as normal. For example:

J'ai besoin de ce fromage.

J'ai besoin de ton fromage.

J'ai besoin de le fromage que tu as acheté > J'ai besoin du fromage que tu as acheté. (This is preposition de combining "normally" with le.)

A similar thing in principle happens in any case with preposition de and there's really nothing special about the phrase avoir besoin de.