No, you're right, but it seems to me that you are also assuming things. Cyrilroy21 and Sandypilot, in his original posts, never limited their search and opinions to "just flight instruction". That's what you assumed, SoCal.
Take a look at the school Cyrilroy21 mentioned, "Aviator College of Aeronautical Sciences & Technology"; the operative word being "College"?? How do you think they offer F1 visas?
Remember,
"Student F1 Visa and M1 Visa - Overview
The first step for a prospective student is being accepted for enrollment in an established school (University/College) which is SEVP certified . In general, for academic students, including those in language training, F1 visas are the appropriate category, and for nonacademic vocational students an M visa is the appropriate category"
So, the only way you could obtain an F1 status from the aforementioned school, you would have to take up a full course of study, i.e. "college".
On a different note, "M-1 visa holders are not eligible to apply for H-1B visa but may apply for practical training upon completion of studies for a period of 6 months." So, technically, M1 visa holders have the option of applying for practical training, if offered.