Under FAA rules this was a screwup. [edit: see my own reply] (However, the rules are subtle, so they can be partially forgiven.) However, I'm not only a dispatcher but also a philosophy BA, so I've found a good way to explain it.

Your reserve fuel (the "extra" fuel over what the actual flight burn) can of course be used (hello, that's what it's there for) but—and here's the rub—you can never plan on using it.

That is to say, in this case, when they missed their first or second approach, they CANNOT say, "We'll use our reserve fuel and make another go at it" because that would be intentionally planning to burn your reserve.

You may only dip into your reserve when you have no other choice. In this case, when the only fuel they had left was reserve, they are obligated by law to proceed to the alternate airport, which clearly they did not do [correction: they did do the proper thing; see my 2nd reply below]. No bueno.

[this is a slight simplification (minor details omitted for brevity) but the kernel of the issue is properly described]