So the chance of false positives is minimal.
It depends on the purpose. For identity verification purposes, when you already have independent reason to suspect that someone is specifically Person X, then a "very low" false positive rate is likely sufficient.
For filtering, however, "very low" isn't enough. Suppose your facial recognition system has a 0.001% false positive rate (one per 100k), but you have a list of 1000 banned faces and your venue sees 10,000 visitors per night. You're making ten million comparisons, and that "very low" false positive rate will still result in 100 false matches.
That could still be okay, if a match just involves (here) pulling the patron aside for an ID verification. Asking 100 people for ID is much more benign than turning 100 people away at the turnstile. MSG here did appear to follow the match with a secondary verification (per the article), but I shudder to think of all the venues that will hear "very low false positive rate" and not really think through the consequences.
I loved your .001% example, I'm going to steal that when I talk folks. We often describe how systems fail at scale and talk about how being wrong 1/1,000,000 times can wildly backfire at large numbers.
All that being said, I just don't want people around this forum thinking facial recognition is some fringe, low accuracy modeling exercise like they used to be. The models are actually incredibly impressive these days.
And the government never makes mistakes.
They're taking an image, segmenting out the face and they're improving an existing model for that individual. Super scary stuff that's going on. (Other than the fact that they have an existing image)
If she was in IL .. she should persue them with the BIPA act.