The paper is available, so feel free to check yourself. BMI was taken into account. Fast food I do not see, but where did you read about this association?
At the end of February this year the FDA banned PFAS in food packaging which was prevalent especially in paper products which held greasy food. If you ate a bunch of French fries there was a good chance you were exposed to a significant amount of extra PFAS. This study could be finding a correlation between diet and PFAS exposure and nothing more. I’m not saying it is but if not corrected for the signal is suspect.
I do not have a link, but have read it in multiple journals.
The MAO is entirely plausible. Many fast food wrappers are lined with PFAS because of its temperature stability and hydrophobic properties. At high temperatures these coatings also leech the coating.