Narratively speaking, this theory isn't very likely. They're unlikely to introduce lore and then say it was just a lie later, because it's a pointless exercise.
Like the elvhen pantheon?
If it wasn't true, they probably would have conveyed it to you as part of Iron Bull's characterization, because it would be an important point if he were willing to misrepresent the Qun for a friend's feelings.
Hissrad's title/job description is "liar", and he obviously cares about Krem's feelings and even gets defensive if you ask him if he's okay with Krem really being a woman.
That's very "not Qunari" behavior.
It's Ben-Hassrath behavior. He is a spy. It is not his role to give bas truthful information about the Qunari that might endanger the homeland.
Not using this narrative point, however, it would serve no purpose but to confuse people about the Qun, where usually they introduce these semi-out of place for the main narrative characters, like Iron Bull and Fenris, just to offer perspectives on places and cultures they plan to use more later. What he said is most likely true. I doubt anything we got out of Iron Bull about the Qun is factually incorrect.
He says things that directly contradict Sten in Origins. Sten states that a woman cannot be a man, yet Iron Bull believes that Krem is a man. Sten also strongly implies that Qunari do not have sex with others except when matched to a mate for procreative purposes. Others have also pointed out how Bull's claim about the cork popping seems to contradict Qunari culture of discipline and not wasting resources.
Most likely, the Qun does believe that those that don't fit their assumed gender roles are simply not of their physical gender. The fact is, the belief that one gender is always going to be better than the other at specific roles is false. It's not true, and it can be pretty easily demonstrated as false.
So what? The point is the Qunari believe that is true.
If they didn't have some way to mitigate this, then a core feature of their society could easily be proven nonsensical.
The Qun would be proven nonsensical if they made an illogical exception to the rule, because not only would the rule still exist, it would be broken in certain cases and yet still not repealed. It would be more logical to simply eliminate the rule, rather than keep it and break it at times.
Is there illogical implications in deciding the exception to the rule is simply not their physical gender, but their gender role? Sure. But it's less illogical than having the clear fact that some men are better organizers than most women and some women are better fighters than most men just there in the open, completely unexplained or addressed.
I think they do address it. According to Sten one gender cannot be the other, and living on the moon is as attainable. So I think the logical choice for Qunari would be to take the female who is a superior fighter, dismiss that reality as a fluke, and stick her in a female role anyway, perhaps finding her second greatest skill and going with that.
I think the problem you're having is that you're assuming the most important thing here about gender in the Qun is the same as in your culture, meaning physical parts. I think that's probably not true to them.
"I do not understand, you look like a woman." -Sten
The most important thing, to them, is the role they fill.
They are given their roles based on their physical gender.
Their role is the most important aspect to them in all aspects of their lives, while the physical is a secondary concern. If they have to bend on one, then they'd rather it be on the physical aspect.
"Why would your women wish to be men? That makes no sense." -Sten
They aren't going to deny physical reality. They are simply going to send the warrior woman to cut flowers instead of necks. She cannot wish to be a man...
"That can lead only to frustration." -Sten