That thing about not applying for aid in subsequent years mostly applies to international students. There are a few schools that do place restrictions on applying for institutional aid for all after year one, if you did as an incoming freshman.
But that has nothing to do with the FAFSA. The FAFSA is primarily used to award federally funded need based aid. It can be completed at any time for purposes of getting a Direct Loan…or if the student becomes Pell Grant eligible…they would get that too.
I agree with the better safe tha sorry approach…unless you are fully prepared to pay the full cost of attendance. It doesn’t take long to complete a FAFSA.