Martin told me where the confusion might come from:
in slide 14/55 we have the general formal definition of formal ("mathematical") grammars (with whatever right-hand-side and no "preterminal"), at the bottom of that slide usual NLP practice are introduced.
In slide 17/55 we clearly indicate that the definition provided there (slide 17/55) is "in the NLP framework" (introducing more concepts than in the pure formal context).
To clarify further with your question here: we can simply change the provided formal CFG into a "NLP" (not so much "natural" anyway! ;-) ) CFG by simply doing:
S --> S S
S --> A S
S --> S A
S --> A
with A a pre-terminal, and
A --> a
as a lexical rule (with probability 1, of course!).
This is a trvial equivalent CFG.
I hope this clarifies everything.