Well it proves that it is possible to sterilize a nebulizer if you follow the procedures.
The rest of the study is less clear I think. Of course if you don’t get your nebulizer clean, your bugs will be on it. But that does not prove in itself that you get (re-)infected by your nebulizer. Your bugs will be all over the place in your house too. Do you sterilize your cups, saucers, cutlery on a daily basis? And mostly: it is very hard to get rid of bugs like PA once infected. So probably these infections will re- occur anyway some time after ending the antibiotics course. The study does not make it clear if an unclean nebulizer contributes to this re-occurence. The fact that exacerbations and unclean nebulizers occur together (correlation), does not prove that there is a relevant causal link. That is not to say that one should not do the utmost to clean the nebulizer and ones daily environment.