I might have misunderstood the case they were talking about.
The main case "Hot Coffee" deals with is the woman who burned herself when she spilled McDonald's coffee on herself. McDonald's wanted a jury trial and so they had one.
You can't agree to arbitrate tort claims. There's simply no mechanism for that. The only claims that can be arbitrated are contract claims, unless
a court system has a mandatory arbitration process for those types of claims -- in which case that isn't the kind of arbitration that you're talking about.
I guess there isn't an arbitration clause when you buy fast food but it seems like the case was supposed to go to arbitration until McDonald's decided on a jury trial.
I'm confident that's not the case. There may have been a settlement offer or even an attempt at mediation (which isn't the same thing as arbitration), but it's impossible that the woman agreed beforehand with McDonald's that any tort claim that she might bring would be handled by arbitration.