I'm not too sure, but I don't think they can access your PC unless you give permission and they won't be able to view your files. They will be able to know when you are using the wireless connection and for how long you've been using it. I'm not too sure to be honest, but i'd accept the offer. You don't 'have' to use it.
You might have trouble picking up the signal, depending on how far you are from the router and how many walls are in the way.