I have heard it said that children growing up with animals are less likely to have asthma. Apparently the kids build an immunity to any of the dust mites etc found in the garbage flying around from the animals. Dunno about the truth in it, but I can see the reasoning behind it.
I've too have heard and believe this. We have 2 outside dogs which Nina absolutely adores, and we're getting 2 budgies which will be inside. I'm not at all worried about this. I know I'll have to keep the area tidy.