They are likely using a form of https://en.wikipedia.org/wiki/Perceptual_hashing

The noise level a perceptual hash is sensitive to can be tuned.

The "falsely match similar looking" is harder than one would expect. I used to work on an audio fingerprinting system which was extremely robust to "similar" audio matching. What sounded similar to us was always identified uniquely by the hash with high confidence.

For example. Take the same piano piece done by the same artists on the same piano performed as close as they could to the same: never confused the perceptual hash with ~10 sec of audio. Not once. We could even identify how much of a pre-recorded song was used in a "live" performance.

There are adversarial attacks for perceptual hashes. However, "similar eyes" would not be one to a standard perceptual hash. More like: a picture of an abstract puppy happens to have the same hash as an eye.

I'd be curious on the details of the hash. That is necessary to know what the adversely attacks are. But I see no mention of the details. Which is suspicious on it's own.