Live Mesh isn't supposed to sync unless you are logged into Live Mesh, but people have reported that if you log in and then log out, sync continues. Since this is undesired behavior, filing a bug would be the way to go, including your logs.
How to Submit Bugs and Live Mesh Logs
As for how to prevent this behavior, short of killing the service, there is nothing to configure since it isn't supposed to be synchronizing unless you have logged in.
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator