B2N2,
The first portion of the OIG footnote you have highlighted is in connection with academic courses and students. Flying training is regarded by the DHS as non-academic / vocational. The M-1 is for vocational courses.
Only Part 141 certified schools can accept foreign students and have the capability to issue the I-20 which is the visa application form.
Formatting added.
...unless an established institution not being a Part 141 center receives SEVP certification and associated approval for its Part 61 (etc) courses.
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A few more checks and balances are being introduced via SEVIS II:
Originally Posted by Overview - Creation of SEVIS II
SEVIS II will generate and displays an admissibility indicator for each F/M/J nonimmigrant that reflects whether they are currently eligible for admission into the U.S. under the terms of their F/M/J class of admission. F/M/J nonimmigrants may view their admissibility indicator in SEVIS II before traveling to the U.S. to confirm that they are eligible to enter the U.S. at that time. To generate the admissibility indicator, SEVIS II uses the information already in the system and a set of business rules to determine if the individual is currently eligible to enter the U.S. as an F/M/J nonimmigrant. SEVIS II will exports the admissibility indicator to the U.S. Customs and Border Protection (CBP) Treasury Enforcement Communications System (TECS) to allow CBP officers to view the admissibility indicator when the F/M/J nonimmigrant arrives at the border and requests admission. The CBP officer uses the admissibility indicator to determine if the individual may enter as an F/M/J.
Overview - Creation of SEVIS II