Identity/statement of educational purpose verification is intended to thwart possible fraud related to receipt of federal funds. Schools aren’t choosing to select students to verify their identity. It’s purely a Department of Education thing related to federal student aid. So no FAFSA, no need to verify identity in this manner.
For instance, I had a student selected who had attended several schools & received federal aid at each in the span of a few years. She had cancer, which necessitated dropping out and changing schools. But ED didn’t know her backstory, so it just threw up a red flag that this student might possibly be running from school to school, collecting aid refunds. In her case, she wasn’t really getting any significant federal aid, but the flag goes up, anyway. She just had to fill out a form & get it notarized. Two years later, her Masters was successfully completed.