Students will also lie about lying. These numbers are incompatible with the numbers that the NCES collects, which are based on applications.
According to PEW (which took the data from NCES), in 2020, 33% of all college students were Black or Hispanic, while 8% were Asian, and 55% were White. There is simply no way to fit 40% fakes into those numbers, or even 10%, and even 4% would have different results.
As for veteran status - same. According to NCES, 5.1% of all students are veterans. So how are 20% faking veteran status, but somehow only 5.1% are actually veterans based on application data?
So yes, these statistics are bogus. The students were lying, but mostly lying on the questionnaire. Either to mess with person asking the questions, because the student believes that OTHER students are lying, or to create an illusion that all students are lying.