Why might an infection contracted in a hospital be more severe than one contracted at home?

Because hospitals are the most disease ridden places on the planet. It's a horrible system. "Let's get all the sick people together, and put them in one building." So for starters, if someone has something severe, they're going to go to a hospital. Well that applies for all the people in the area, so there are lots of germs for severe diseases in hospitals. Furthermore, like I was saying, hospitals are cess pools of disease, so it's not so much that you might contract a more severe disease, but you might contract multiple diseases at once even.