Hmm, does that anonymous ID change? If not, it is not going to stay anonymous for very long as patterns will remain largely unchanged. People do tend to be creatures of habit.
I mentioned location data and if there is one thing we have learned over the past decade or so, it is that location is not gathered just from GPS ( which is the argument I assume you were making ).
edit: As for the claim, no data is sent over the internet.. I just plainly do not believe that statement. I do not understand how anyone would.