There are a lot of situations around asthma that folks need to understand that have bearing on fitness for service:
1) Asthma is a medical condition - not a disease. I can be induced by a variety of factors, many of which can happen on a battle field and not necessarily under "normal" workout conditions. Low temperatures, allergies, and pollution are all triggers of the condition.
2) The military doesn't want to see it occur regardless because they cannot control the battlefield. A soldier/sailor/airman/marine who can't breathe is another casualty to be evacuated exposing others to additional risk. Not something ANY dedicated soldier/sailor/airman/marine wants to do to his/her peers.
3) That being said, many asthma diagnoses are questionable. Often inhalers are prescribed for conditions similar to asthma but definitely not permanent. Examples include bronchitis from a upper respiratory infection (bacterial/viral). Patients are impatient for their conditions to improve, as typically this is not necessary for the condition to heal. It can help a slow healing condition heal faster for the patient. It is a temporary condition that should not recur in most individuals. Some doctors may write Asthma on the medical records to assure the prescription is approved by the health insurer when it is really bronchitis. Little does anyone (doctor or patient) realize that they are putting a future officer candidate in a tricky situations.
That being said, the military does not like taking unnecessary chances and doesn't necessarily have the resources to sort out the good and bad diagnoses. If a candidate does find that s/he has a questionable diagnosis, they should work with medical professionals to correctly assess the condition optimally as soon as possible, but even afterwards, if further testing is necessary to correct a diagnosis, this should be taken proactively. The folks at DoDMERB do look carefully at medical records when a condition is brought to their attention, but respect the professional opinions of the doctors who see the patient. If a misdiagnosis is confidently corrected with adequate documentation, it should not be held against the candidate.
I encourage the young folks here to think about what is best not only for your own career, but those of those who will have to share the burden of protecting you, should you fall ill on the battlefield. Not to mention that you could DIE of an untreated asthma attack if you are in a situation where you cannot be extracted to adequate medical care.