I am so happy that your instincts were right. I had an opinion of course, but I can't give medical advice. But now that the decision was made, I will comment. If this was me -- I would know this was asthma as a result of the inflammation caused by the illness he just had. The clues were all there. Yes, it's possible that he had a bad respiratory therapist, but usually after 3 times they get in the neighborhood. And if you really feel that Ethan didn't blow as hard as he could, I'd make sure that it was accurate in the future. So I suppose that's a good lesson too.
I just went through something similar. I had "cold-like" symptoms after exposure to pollen. It went quickly into my chest. My Fev1 dropped 10%. (My last several cultures are not picking up Pseudomonas that I always have cultured). My doctor gave me a cortisone shot and Zithromax -- my doctor was telling me the latest studies show Zithromax in addition to being an antibiotic and an anti-inflammatory it also has an effect on the immune system in a unique way. Today, 2 weeks later, my FEV1 is back to baseline and all symptoms (knock wood) are gone.
I am so happy your son did not needlessly have to go into the hospital which is not pleasant plus the addition of picking up new bugs. So all is good!