Well there is one or two possibilities.
A/ Since there was no culture the wrong anti-biotic may have been prescribed, sadly just like with human, dogs or cats anti-biotics are often wrongly prescribed or just because. A culture should ALWAYS be done, RI are not always RI and RI are not all equal there are different types of RI
B/ There was no RI in the first place some animals have been known to make similar sounds without it being a RI (nasal cavities issue, stuck shed)
Bottom line it's impossible for us to tell, but one thing is certain either change vet or DEMAND a culture next time around.