Any time you show > 1 confidence interval there is a multiple test risk. As an aside, multiplicity adjustments are controversial when you really have marginal questions, e.g., questions targeted to one time point at a time. The best approach is to figure out how to compute simultaneous confidence bands that “protect” against an infinity of hypotheses. These will be a little wider than the intervals we see at present, but not as huge as you’d think. Something like using \alpha=0.01 for a 0.05 simultaneous band. Could base this on Kolmogorov-Smirnov type of ideas.
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In any case, I understand our default should be to use adjusted curves (Cox if PH assumption holds or parametric models if not). Sometimes, if the variable of interest (i.e: treatment) does not satisfy the PH assumption, stratifying by that variable may be the way to go, but no statistical tests for computing survival differences can be used, right? (as in Califf et al., 1989). Thus, it may be useful some provide an overall log-rank test and compare survivals at fixed time points.
I am dealing with a similar situation (early high risk in one treatment arm, late high risk in the other, PH assumption violated) and I have doubts about the right approach.