Comma before "and" in "that" clause?

The Chicago Manual of Style (16th edition: 6.29, page 317) would disagree with Grammarly. In the section Commas with compound predicates it states:

A comma is not normally used between the parts of a compound predicate—that is, two or more verbs having the same subject... .

• He printed out a week's worth of crossword puzzles and arranged them on his clipboard.

It says also:

A comma may occasionally be needed, however, to prevent a misreading...

• She recognised the man who entered the room, and gasped.

In other words, she recognised... and she gasped. On this basis it seems to me that including the comma actually makes the sentence potentially ambiguous. It could be interpreted as:

• I also remember that... and I rigorously proved...