While I cannot speak for other people who call themselves mediums, I can say in my own experience as a medium that animals and people bring through much more detail. This includes what they looked like in life (including breeds if applicable), how they passed, specific memories (houses they lived in, jobs they worked (for people), activities they enjoyed, etc), what they were like (personality), and much more. This first set of information can be validated by the recipient and/or by those who knew the deceased. After the identity is established, the deceased then bring through detailed messages for the recipient and/or those who knew them.
I am sorry to hear you had such a vague and disappointing experience with someone who called themselves a medium. If they really were a medium, they did not do any justice by you, your friends who lost dogs, or the animals in spirit, and they were most likely untrained.