....No matter what no set of circumstances is going to:
1. Effectively turn your body into rubber giving you the ability to stretch and contort your body into any form.
2. Give you the ability to spontaneously combust into a being of fire capable of extreme temperature levels.
3. Give you the ability to render themselves invisible.
4. Give you the ability to create/project forcefields.
5. Give you the ability to alter mass and biology and become a walking creature of rock.
Yes, it takes a effort to suspend disbelief. But suppose you are a viewer game to make the effort. Then, you accept that cosmic rays in low Earth orbit did do these incredible things. After all you saw them on screen. Easier to suspend with good FX, but a willing imagination can help the shoddiest CGI, no? But at the same moment you are to also to remember and accept that cosmic rays did not do any thing like this to any of the other many people who've gone into orbit!
You are asked to believe cosmic rays did and did not do such things.
Asking willing suspension of disbelief is one thing. Demanding willing suspension of critical faculties when faced with a self-contradiction is quite another. I think the latter is bad writing.
IIRC it was a special condition of cosmic rays, higher than normal or combined with the equipment or something like that. Needless to say, I don't think it needs to be "explained" much more than a handwaving. It's rather small and insignificant part of the story, overall.
In Nolan's more "realistic" Batman movies we've got microwaves that causes water to instantly turn to steam (yet not harming the people around who are also made up of mostly water) and a man with severe burns able to pretty much walk around for the better part of a day without being in agonizing pain or dying from severe infections. (Not to mention having a useful eye.) Shit, when foregoed medical attention he wasn't even in an isolation ward!
I think we cannot examine these things too closely. How did the Fantastic Four's exposure to cosmic radiation impact them and not others who went into orbit before them? It was simply the fall of the cards and the roll of the dice. They went at precisely the wrong time. Like all of the Apollo astronauts who managed to survive exposure to radiation outside of the Van-Allen Belt, it just happened to be at the right time with low solar activity. If that calculation would've been wrong they would have been irradiated to death.