I'd agree about kids on farms - my oldest friend lives on a farm, three kids, all incredibly healthy despite living with a menagerie of dogs, cats, poultry, horses, cows and various other beasts along the way.
DH has asthma which is still triggered by longer haired dogs, cats and horses even though we have three dogs at home - we have greyhounds who although are short coated are definitely not non-shedding! I/we make a point of housekeeping with his allergies in mind - so no carpet downstairs, regular damp dusting, frequent hot washing of dog duvets, quilts, sofa covers etc, plenty of airing and so on. Paradoxically, although there may be more oomska coming in to the house, it is probably cleaner because we have a more aggressive management programme for it. When we didn't have dogs, and had carpets, I'd only hoover once a week sometimes, now it gets done at least every other day, and sometimes more often depending on visitors/amount of crap.
We find that when we visit friends with horses/cats etc, that he does start wheezing/eyes sore/sneezing etc - I suppose the question is what would have happened if he'd been exposed to animals as a boy? Fortunately, I was exposed to a wide variety including horses, dogs, cows, poultry, guinea pigs, rabbits and cats and have never had any problems. It's a really interesting issue, especially as lots of kids today seem to spend a huge amount of time indoors, which I don't think is healthy. Maybe kids with dogs are also getting outside more? For walks and play?