After describing the problem to the students they called me the next day, pointing out that I was asking a weird question (although they were very polite, that's what I thought at that moment
). Basically I was asking for confidence intervals on something that wasn't a stochastic process - I had just one fixed set of data. So, they said, we can tell you that with 100% probability you had a sharpe ratio of x in the past. I know, I said, but what about the future? That's how we got from the original problem to the one they solved.
I'm still a bit uneasy about how they generated the new time series, because now the problem shifts to "how confident can we be that those new time series describe new possible futures". In a sense the whole process left me more confused than I was before.
I guess the difference with testing whether a cure is effective is that the way people react to the cure shouldn't be dependent on time. The way a strategy reacts to the market is something that changes, because the market changes over time. That's why you can do a statistical test on drugs, but it gets a little trickier in "our" case. Not sure if this is a good analogy, but it makes sense to me.