This is not like investing money in a hedge fund where there are hundreds of competing possibilities. Cryonics Institute or Alcor, pick one.

That only holds if you assume there exists a viable cryonics option. When making a decision like this, an important question to ask is: "Am I being had?" I tend to think both organizations are probably legitimate, but their legitimacy or lack thereof is fundamental to the rationale behind signing up for cryonics in the first place, and not easily dismissed as a "flaw".

But lack of the information you're demanding just isn't something that should stop you from signing up with Alcor or CI.

The above reservations aside, my point wasn't really that it should stop you from signing up (hence "The issue isn't so much the accuracy of those claims, but the nature of them"), my point is that it seems very rational to obtain that information in the course of evaluating your options, and if you can predict that you wouldn't bother to do so, you've possibly identified an irrational operator acting on your decisions.