Answer
According to many visitors, there are indeed noticeably fewer stray dogs in Uruguay than one might expect based on experience in other countries. In everyday life, something else stands out more: a great many people have dogs of their own, and pets are a common sight in urban areas.
The claim that “there are three dogs for every Uruguayan” is more of an emotional way of describing the scale of people's love of animals than an exact statistic to use in personal calculations. But it conveys the impression well: dogs are an ordinary part of city life.
For those moving with a pet, this is generally a benefit, but housing, veterinary care, food, and the rules in a particular building still need to be addressed separately. A friendly attitude does not mean that every landlord will automatically agree.