Don't forget that Facebook's false positive rate should be very low. There are lots of humans on their platform, and they should all pass the test.
This makes it easier to construct a bot that will pass the test.
I can imagine it would be easy to trick the system a few times (either as a bot pretending to be human, or a human acting like a bot), but tricking it consistently over months or years is going to be damn near impossible.
I've only given it a few minutes thought, but position and time data is really small, and easy to compress (you don't need to send anything while the user isn't moving the mouse). If it's sent in batches or over an already open websocket, it's not like it's using a ton of resources on the client.
Assuming all of their users (guessing a billion daily active users) are on desktop half of the time (a wildly incorrect assumption I'm sure), and the mouse position data is 1mb per person for the data you care about (which again, seems like a lot), that's 500tb.
For $25k you could store it all. That's nothing compared to the benefits of being able to identify bots on your platform.
Using these metrics you could probably start to draw some characteristics of how your mouse acts based on what you are doing and where you are moving your mouse.
This could then probably be used to build some form of algorithm that moves the mouse for you with noise (accelerating up & down along the way, deviation from a straight line, stopping in the middle of the line, etc.).
You need to break ReCaptcha? Simple, you implement your own captcha on your own site that's frequently used and whenever you need to solve one you copy the challenge and present it to one of your users.
Same with recording mouse data.
It's an old idea even, very similar to https://xkcd.com/792/
You don't need to learn from all humans. You need to learn from very few (or just even one).
Not all problems are machine learning problem.
At least the mouse movements themselves shouldn't be difficult to do given a source of data. Simulating that you click on same FB UI elements as real people with same statistical properties on other hand is where you might be lacking the data to do it properly
This is a cartoon version of deep learning.
And even if the bot author had all that information, it would still be super hard to write an AI that accomplishes a given task in a way that mimicks a human successfully. It would mean to win a 'mouse turing test'.
What the API returns is under the control of the user. So the API does not help FB to fingerprint you.This issue touches on the real privacy problem the net is facing. It's not the wrong cookies or privacy policies. It's fingerprinting. There is no technical solution to it.