Ambiguity with negative clauses

"He didn't run because he was afraid."

CMOS says that a comma is advisable before "because" in the above if you intend the meaning to be that the man did not run at all. A comma avoids ambiguity. Without it, it reads that the man still ran, but for a different reason other than fear. ("He didn't run because he was afraid; he ran because he was late."

My question is, does this apply to all sentences that start with a negative clause?

"I would not recommend this, because..."

"I can't do it, because..."

etc.