As far as I know, the time machine share is set to public for ease of setup, however you should be able to set it up as private and assign an user to it.
Based on your response about the public folder open to anyone on my network, i guess Time Machine needs to be able to place its data anywhere the user chooses on their own network.
I have no issues with leaving things public on my home Network as long as I can be sure Ive closed the gate at the router.
So now need to see how my devices are uniquely identified through the router, is it IP address and mac code?