The SF AIRPORT FD/ARFF crews made a mistake while responding to an emergency.
The crew of Asiana made a mistake while conducting the most basic kind of landing.
Asiana had all the time its fuel allowed to make a good landing.
ARFF at SFO had minutes to attempt to help those in trouble.
YES, ARFF/SFO made a huge mistake.
AS to traditions. Being a native born SF I can assure you that we are reminded every year during the ceremonial painting of the golden fire hydrant. And if you don't know what this means, you can look it up yourself.
Sadly, the traditions of ARFF/SF FD fell short.
Even sadder the traditions at Asiana never existed in the first place, at least with regard to the most basic type of landing there is.