bathroom door open

Question

Hi, A friend tells me that his wife told him that if the bathroom door is open the entire house is considered like a bathroom, and you cannot say a beracha. Is this true, or another case of going overboard? I ask because my dog has a habit of going in to drink from the toilet, and if the door is not blocked open it will close behind him automatically and he'll be stuck and scratch the paint off the door trying to get out. Thank you, Sammy