Are they offering to fly you out there? The responsibility thing is a valid point, the big question would also be whose medical license would you be working under (though once you are overseas you can't officially practice as an EMT, you'd be more of a first responder providing care until the local rescue service arrives.)
That being said it's not like it's a SWAT team or pro football team. Seems to me pretty low probability of a ballroom dancing team having a serious injury. Easiest thing would be to run it though the university, they should have pretty standard forms for physicals, waivers etc. And if the team is willing to put in writing that they understand you are not a doctor, would only be providing stabilizing care etc etc etc might not be a bad deal.