The difference is that grabbing it pre-FTA is also grabbing a perfect copy. The quality may not matter to many of us, but to some it does. And because it matters to some, major copyright holders have started to treat unlicensed exchanges as “competition” from a business PoV (which is a concession from strictly seeing it as crime). So their business strategy is to compete with the unlicensed channels by offering perfect quality media at a price (they hope) people are willing to pay (also in part to avoid the inconvenience and dodgyness of the black market).
FWiW, that’s their take and it’s why they get extra aggressive when the unlicensed version is perfect.
Why would a browser handle it incorrectly for one video on one invidious instance, but not for most other videos and other instances?
Note that I’ve seen this broken behavior both in my own Chromium installation as well as Firefox in Windows as a public library.