Let’s offer some correction to the language used here:
Running the vent fan while flushing the toilet MIGHT cause odors to be drawn into the camper.
The AAV can fail and MIGHT cause odors to be drawn in.
Too many factors at play to use the word “WILL” when describing these situations.
In my case...
During warmer weather, as the black tank fills and there’s relatively stagnant air (no wind outside), odors can become more prevalent when flushing the toilet. A proper functioning vent relies in some part on having a little bit of air circulation. Kinda like how a chimney may not properly exit the smoke if it’s not above the ridge line of the roof.