Planes make unscheduled stops for fuel on supposed "nonstop" flight all of the time.
I think the key word there is "unscheduled". The first article says that one airline had to do it twice in January and another airline only did it once all year. So it's not something which happens often. It also explains why they sometimes have to do that.
The second article says that "dozens" of flights had to make stops - it doesn't say what percentage that is - but it also explains why and it's clear that this is the exception rather than the rule. You have to subscribe to read the whole thing.
The third article is not accessible from the UK for some legal reason.
I have never been on a non-stop flight which has stopped. Clearly it happens sometimes but the idea that they "do what they like" is ludicrous. The airline industry is highly competitive, any airline that "did what they liked" would quickly go out of business as people would use alternatives.
I'm not clear how you think any of this helps FE theory. Are you trying to cast doubt on the whole airline industry? Are they all "in on it" too?