I think he has a valid argument, and has chosen a good way to make his protest. I also respect the Head for his calm response and for saying that they will consider the uniform rules again. This sounds like a really positive story to me.
I see nothing wrong with allowing students to wear shorts - as other posters have said, you could specify length and say that they weren't to be tight shorts/hotpants.
At the senior schools that ds1 and ds2 used to attend, the boys had to wear blazers, and even on the hottest of days, they had to obtain permission from the teacher to remove their blazers - and some teachers used to refuse to give permission. I never managed to find out what possible reason they could have for such a refusal - or why they thought it was a good thing for the boys to be sweltering in their blazers instead of working comfortably in shirtsleeves.
Thank heaven the school they go to now has a more sensible policy.