I think this approach is a bit disingenuous. Her claim is that since we can't directly observe black hole evaporation, we can't know which mathematical model is "correct" in describing the phenomenon and that we're therefore just left with picking the explanation that we personally like the best.
This same argument can be made about a ton of things. For example, we have yet to observe free quarks directly (due to confinement in QCD), but I don't think people are saying that the quarks model is just the one that we happen to find most pleasing. The reason we are confident in the quarks model is because it makes all sort of other predictions that we can confirm.
Who is to say that the various ways of resolving the BH information paradox are indistinguishable simply because we can't observe the evaporation directly? Maybe they make other predictions as well.
Generally, I think that we need to be skeptical of various speculative ideas and in many ways we have strayed off course for a while in theoretical physics, but I don't think the answer is to just explore topics and theories that are completely grounded in observations and experiments.