French has an interesting word which somewhat clarifies this situation: "si" (not the conditional "if" in this case).

For lack of a better explanation, it's essentially a negative "yes", used to negate a negation.

For instance:

  A: "Don't you understand?"
  B: "Si"

Meaning "No, I don't agree with you, but yes, I do understand".

I find it very simple yet quite powerful.