Speaking as someone that suffers from gender identity issues but couldn't explore those feelings properly when I was young due to being brought up in quite a strict household with a father that abhorred such ideas it's a hard one for me, I have never really felt strongly that I'm any particular gender, gender isn't binary, it a scale, mentally I do not see myself as a man or a women, in truth I feel like I'm both at the same time, it's very confusing, for me it actually got
worse when I hit puberty, I felt like nature was forcing me to be something that felt wrong, one gender, a man, that was a very confusing time for me, it's a strange feeling existing in a world being physically a male while in your head you don't feel you are one, it makes you very aware of how social dynamics are effected by physical gender because so many people make assumptions about you based on your gender, in school, "oh, you have a willy, your playing rugby today," "err no, I prefer to play netball please", "lol, get changed now young man, rugby will put hairs on your chest"
I've reread the op a few times now and personally I don't see the issue as long as the parents don't force a gender on him, which they don't,
"We still put some neutral clothes in his wardrobe if he ever decides he wants to wear them."
"We leave it up to him to decide what he wants to do - if he changes his mind and wants to be a boy again then he does, but if he doesn't, he doesn't."
Remember that they also thought that it was just a passing phase just as few on here presumed but it obviously wasn't, you have a child that is wanting to cut his genitalia off, that is very serious, any sensible parent is going to have their child accessed under these circumstances rather than force their child into a gender type which could do more harm than good.
Although that being said I don't think the diagnoses at this young age should be 100% set in stone, and being that the child has not reached puberty it should be a guideline open diagnoses, although I still see nothing wrong under these circumstances to let the child to choose to live as a girl, I'm no professional but with the limited information we have based on this case I'd conclude that it would be detrimental to the child's mental health by forcing the child to live as a boy.