My initial guess was something like the fingerprint is stored as a bunch of samples of where there are "hills" on the finger, and verifying the fingerprint cons

My initial guess was something like the fingerprint is stored as a bunch of samples of where there are "hills" on the finger, and verifying the fingerprint consisted of checking that those hills are present - another human will have valleys where the first person had hills. The gel screen protector presented 100% hills so all the checks passed. What they needed to fix was to check for the non-presence of some "valleys" as well. Of course the fact that they're using hashes of the fingerprint means this theory is bogus and the issue is probably a lot more complex/involved.