3) is an incorrect assessment. As an example it is very easy to generate 500 random data points sampled from a normal distribution mean 0 variance 1. It is much harder to go in reverse, taking those 500 points and saying "these come from a normal distribution mean 0 variance 1".
Point is that the random number generation problem is significantly easier than the random number modelling problem.
One possibility: Record a human mouse movement, and then just reuse that same movement every time. For them to search a database of all used movements would be prohibitively expensive.