I have always wondered about this and why they allow the animals in

There's no problem with letting the animals in, it's a matter of what a person should always do after touching a pet; wash your hands.

If you read the article, the problem is not that the animals are bringing organisms in – the animals and their handlers tested clean before they entered the hospital.

The problem is that they're picking up organisms from the patients. Even if you prohibit therapy animals, cross-contamination is a problem. Many hospital-acquired infections can be traced to people's failure to wash their hands often enough or thoroughly enough.

They do say that hospitals are the dirtiest places. Always bathe the dog after a visit to the hospital.