There are a lot of factors here.
One is that the definition of asthma is a little fuzzy. It ranges from people who only have discernible abnormalities when they are having a viral illness ("reactive airways disease") to people who are dependent on multiple medications, taken each and every day, to be able to maintain the ability to walk around normally. Obviously, people at that end of the spectrum shouldn't dive, period. It is questionable whether people at the other end actually even have asthma at all, and certainly, it seems as though between their incidents, they are probably quite safe to dive (as safe as anybody -- we don't think twice about allowing a 50 year old 2 ppd smoker to dive, without doing pulmonary function testing).
So we start with an unclear diagnosis, and then we get into the controversial nature of where to draw the line on diving safety. It used to be that any diagnosis of asthma was felt to be a complete contraindication to diving (just as diabetes was), but things have loosened up a bit. However, to my knowledge, there is no universally accepted set of criteria for "acceptable risk" for diving. I know what the folks at Duke use, but when you face the average GP with the question (or even, I would imagine, a lot of pulmonologists), they are not going to have solid guidelines to make a decision.
And then you get to the whole fact that diving is NEVER completely safe, and that diving as an asthmatic is somewhat less safe, but it is probably impossible to quantitate that risk (since nobody is going to do the study of taking sets of progressively more severe asthmatics into the water, to see where you start getting gas emboli
). When you go to a physician and ask, "Is it SAFE for me to do this?", you are asking for a kind of insurance which some physicians are not going to be very happy to give. And we vary as individuals, too, in our degree of risk-aversion. I would prefer to be able to tell someone, as best I can, what the increased risks ARE (which in some cases aren't really known) and let them decide. But they, and the shop or instructor or agency or dive operator, are asking ME to guarantee that nothing untoward will happen. That's hard to do. If the person embolizes, did they do it because they poorly controlled their ascent, or because they had asthma? How do we really know?
And finally, we have the litigation-rich society in which we live, where every doctor gets up every morning with the knowledge that something he does today, even with the best possible intentions, could embroil him for a couple of years with the legal system, at enormous cost of time and possibly money and definitely reputation. We learn pretty quickly how to stay out of legal quagmires, and one of the ways is never to tell anybody that they'll be fine, or this treatment will work, or this activity is "safe". You can't really blame us. Statistics tell us that it is not WHETHER you will be the object of a malpractice suit, but simply when.