Pets tend to be smaller than humans, so manufacturers could ensure that pet MRIs don't drag down human MRI prices by making smaller MRI machines that only work for pets. They probably do.
The bores are really small: 55mm or so is not uncommon, so a mouse would fit, but nothing much bigger. Other animals are usually scanned on a machine meant for humans (sometimes even the exact same ones, very early in the morning or late at night).
Re: the large patient, yikes!