Right, this is what I mean. In this case you have a two models (what you call, estimate of the survival function, and a random variation around it. It makes perfect sense to talk about a null and an alternative hypothesis. H0 being, the differences are only due to the said random variation and we have one model describing both data sets.

You talk about the "true" survival functions , of which the observed values are realizations of, compounded by some random error, which is modelled BTW.

This is all perfectly legit.

It also means you can not apply this reasoning to a simple comparison two curves, without the knowledge of the underlying statistical midels. - you have no concept of the "true" curve and definitely no idea of the random errors - so, no sensible definition of an H0 and Ha.