not correct
no flight instructors will be allowed to work in the US in other categories than J2/H3 (max 2 years). yes, you COULD apply for an H1B, but to get an H1B you need employment authorisation which involves that the school have to PROVE that they CANNOT find anyone in the US for the SAME position, it involves spending money on advertising for at least 3 months etc etc. There have never been as many flight instructors as now, I bet the US immigration knows this as well.
I have lived in the us for a while and I know the rules