Nobody's saying he didn't have the authority, nor that he didn't have a good intention.
BUT... he also gave an example of simply disregarding the rule, instead of using his legitimate power to actually change the rule. That is, he could/should have first formally legislated, "From here on in, you can wash the feet of girls/women".
But he didn't, he just did his own thing on the spot.
The EneMedia have apparently latched onto this as a signal for "Whee! The Catholic Church has declared a New Age of No Rules", and in fact, some of the looseygooseys amongst the liberal clerics are sure to see it just that way ("Yahoo, the Pope disregards rules for the sake of compassion, and so can I. Next up, I'm marryin' lesbians...")
They're wrong, of course, but that's the Zeitgeist.
In sum, this would not have been the Pope's intention, but this may be the result. There are a lot of overexcited looseygoosies out there, who could turn this into another poop-typhoon like the one in the immediate aftermath of VII. We haven't even finished repairing he damage caused by that one, and people are afraid of "Here it comes again!"
I hope the Vatican’s official comments have made clear that the Pope is entitled to bend the rubrics, but that this effects no change in the duties of all other priests.
In the Novus Ordo, for many years, it was incorrect, at the “Ecce Agnus Dei,” for the priest to hold the Host over the chalice (rather than the paten), as in the Old Mass. (It is now okay.) JPII did this at least a few times when celebrating an N.O. Mass. Even if he did it by mistake, it was correct, because he was Pope. The liturgy is whatever the Pope chooses to do or happens to be doing.
“But he didn’t, he just did his own thing on the spot.”
He did not do it on the spot. It was announced earlier that he would wash the feet of both women and infidels. It was also announced that it would be closed to the press.