@Nicole299: It sounds a little suspicious if the guest sent you a screenshot of only the ammenities section. Are you sure they took the screenshot of your page and not someone else's?
In today's society most guests expect internet. To cover yourself in the future add in that internet is not available in the "The Space" section and maybe even in your house rules since the guest has to agree to that before booking your place.
But that brings us back to your particular problem. I don't know that there is a solution to your problem as it is going to be a he-said, she-said situation. You may just want to eat this one and offer them a discount or something. If you know your neigbors pretty well you might call and ask one if they can provide a guest password to their internet for a night.
Whatever agreement you finally settle on with them, they will probably give you a reduced rating review. Above all keep your own review professional. Short and sweet is probably better. Future guests will be reading your response as much as the review.