The main reason is that you already have a pet of your own and we feel it is preferable for fosterers to have no other animals at home.
I never heard that reasoning before.
In my personal experience, I've found that introducing a pet to a home where another pet is already there is a good thing. The two pets keep each other company, so the humans in the home don't have to be there all the time, and the old pet takes on a parental or older sibling role in relation to the new pet.
Their statement is kind of like saying that someone who already has a human child shouldn't adopt.
ETA: When DH was a child, his mum took in foster children and they all lived together in the same home. I guess they are lucky they weren't dogs or cats.
Regarding "special care" - my ex and I both worked full time and had a cat with diabetes and one that was deaf and had a heart condition, a thyroid condition and was completely deaf.