Humans can detect 10ms of latency easily. The problem is more than just reacting slightly later to events, its also how quickly the game/system responds to your inputs because its a round-trip interaction. This ends up usually being where the latency becomes more noticeable to most people. People can generally adjust for consistent latency, but any latency gains are pretty noticeable once you get used to looking for it.
Also 10ms ends up being close to the average input latency of a single additional frame at 60fps, and you just have to look to the efforts that have gone into Super Smash Bros Melee (especially in netplay) to see how far people will go for a single frame.
Practiced musicians begin to feel discrepancies in time starting at latencies as low as 10ms. I learned this when investigating whether bands could practice live over the internet (spoiler: most of them can't). Turns out that due to limitations of physics, even absolutely optimal connections still have enough lag/jitter to ruin it for professional instrumentalists.
Also 10ms ends up being close to the average input latency of a single additional frame at 60fps, and you just have to look to the efforts that have gone into Super Smash Bros Melee (especially in netplay) to see how far people will go for a single frame.