The cursor movement story seems to be a smokescreen to dilute the fact they're actually running an internet wide monitoring network, tracking users from site to site and building profiles on them.
Then I logged into my gmail account and yes it worked.
So you're probably right about that smoke screen and it has nothing to do at all with mouse movement.
My fx browser deletes cookies at exit and my IP changes frequently and I think that's the true explanation for the outcome of my little test.
Also makes me think that they can dump the whole charade and provide no security check at all, but that'd probably make the service-providers uncomfortable and they lose the user as a source of human-intelligence for classifying things on google image searches.