If you believe your BS meter goes off easily, you will soon find it on full time. It is a bad sign when an applicant is contacting you and does not even know your requirements. Even though it is in the ad they will still ask you about the dog, how many bedrooms, if there is a garage and on and on. If you do not want pets in your rental, not only should you refuse them but do consider anyone who even owns an animal. Because as soon as you are out of sight that animal will move in. You are right to believe it will not be disposed of in some manner. You are right to reject pets because pets always cause trouble and cost money.