The definition of mishing (as I understand it) is that you don’t eat stuff that was produced outside of your home/ without your supervision. So whether you’re eating someone else’s food or food from the store, it’s the same thing.
The idea is that when it comes to Pesach, where the ingestion of the slightest crumb of chametz involves an automatic issur d’oraysa, you don’t want to rely on anyone else. (Even though “one person is believed regarding an issur” … but Rav Pam (or it may have been a different gadol) said that to refrain from chametz on Pesach is something that is dependent on mazel (whatever that means*). When it comes to your own mazel, you have no choice but to rely on it. But why should you rely on somebody else’s mazel?
Obviously, every person has free will, but there are times when a person could eat chametz through no fault of his own. Example: There is a worker in the factory who didn’t wash his hands after lunch, and a crumb of bread fell into the food. And you had the bad fortune to buy that food and eat it during Pesach. Or let’s say you opened the window on Pesach and some crumb of chametz flew in and landed in the food. It’s not your fault; you just happened to have bad mazel.