I know that for people from Spain, the Goverment cover all the expenses -- that's because we have a public healthcare system.
For people coming from other countries, it depends in which kind of healthcare collaboration agreement exists with Spain.
I don't know what the situation is for tourist from the USA, but as an example I've read that people from Australia may get in troubles if injured in such a risky activity. Here you have an extract from an article published in "The Australian":
"INSURANCE companies have warned they will not cover Australians who engage in "needlessly" risky behaviour while travelling overseas.The warning comes as an Australian woman, identified only as "J.E", remains in a serious condition at Pamplona's Hospital de Navarra, after being gored by a bull in the back during the annual Running of the Bulls, suffering multiple rib fractures and damage to her right lung. "AAMI specifically excludes the Running of the Bulls," said AAMI corporate affairs manager Reuben Aitchison. "A lot of policies would exclude any claims relating to that event."
P.S.: The most of the English-speaking people I've spoken with in the Sanfermines comes from Australia or California ;-)
Max, if you finally come to Pamplona we should play a "Where is Waldo" like game trying to find you in the crowd!! - LOL
I should note that there is a lot of fun in San Fermin beyond "The running of the bulls"!! For all of you that may be interested in coming here, you'll find more info in this link -- we have already started the countdown for next year "fiesta"!!