What they SHOULD do is to--
1. Scan biometrics. They should not restrict themselves to just irises, because not everybody has irises or eyes. But they should only scan things that you can get surreptitiously without too much work... meaning things that everybody gives away anyway just by walking down the street.
2. Bind the biometrics to keys generated only for that purpose, and never used for anything but attesting to other keys... in zero-knowledge so that you can't associate different sub-keys attested by a given master key.
3. NOT bind the biometrics to names or any other information about the person.
4. Go right ahead and publish the biometrics themselves, together with the associated public master keys. Because again, they are not things anybody should be thinking of as secret... and pretending you can keep them secret is foolish even if you don't put them in a database.
5. Stop centralizing the system that attests to the bindings given in (4); do the work to eliminate trust from that. Or at LEAST don't go out of your way to RELY on a centtral authority.
Once you have that, you have all you need for Sybil resistance, which gives you the global uniqueness they need. Then go build your crypto system on top of it.