I think you are being a bit sensitive, I understand why, but there is nothing to be ashamed of. Rent is expensive! Plus tres exotic, where are you from, where are you going, aren't you interesting.
The neighbour who said "Maybe we shouldn't say anything yet because they are renting", couldn't that just be "Oh well they might be passing through for a year, it's not the next thirty years, so no need to make a fuss or upset anyone"?
For the person who said they didn't want to contact your landlord, well maybe that was just a "Can we sort this out without causing you any problems". If you owned (i.e. the bank owns the house and your soul, I own and it's not that fancy!), maybe the opener would be "I don't want to call the police/animal control/a therapist as your dog is driving me out of my mind". It's just who they call.
Relax and be friendly, your neighbours will appreciate you for you. Maybe send a card to the person who brought up the problem saying thank you for letting you know, terribly sorry again and hope all is better now. Classy reaction from you and no matter what their starting point I'm sure they will appreciate you being warm.