"an additive called TBHQ, or tertbutylhydroquinone, which at high doses can cause nasty side effects in rats (mmmm … stomach tumors)." Wonder if it's cumulative?
http://eatocracy.cnn.com/2014/07/17/what-exactly-is-in-mcdonalds-french-fries/?hpt=hp_t5
Anytime you see "high doses", you need to ascertain what that dose is and how many of the given product (in this case, McD's fries) you'd need to eat to ingest that amount.
At the extreme, high doses of vitamin C can cause blood clots, heart-attacks, kidney stones and blood toxicity. Would you tell someone they better not eat oranges? Or do you take the time to realize that it would take 40 oranges to even start to reach unhealthy levels, and closer to 60 before you really risk these more severe side effects?
In the case of TBHQ, you need to eat 11lbs of chicken nuggest to get to 1g, which would make you feel sick. You'd need to eat 5 times that amount to have a fatal dose. Plus, it's filtered by the digestive system, so it doesn't build up in your system.
So, eat no more than 10lbs, which means keeping your chicken nugget meal to less than 230 nuggets. If you can manage to scarf down less than 230 nuggets, you'll be just fine. Somehow I think you'll manage.