There are other reasons to suspect that the word “Filed” doesn’t mean “Accepted” also. The “Office Use Only” portion of the form to request a birth certificate shows indices for HBC (Hawaiian BC), DBC (delayed BC), NR (no records), and Pending. The office worker is supposed to check off which indices they’ve checked for a BC.
Hawaii statute also provides for the state registrar to send back certificates which aren’t complete and are not being actively pursued. Those are documents they have at the state registrar’s office - presumably in a file - but that have not been accepted as having legal veracity.
The DOH’s own Rules of Practice and Procedure say that “Date filed” is the day that a record is received in the office - unless it is received after 4:30, in which case it is “filed” the next business day.
When I was doing BCs (not in Hawaii and, as usual, acknowleging every place follows different regs), "accepted" is when the document arrived/accepted into the office. "Filed" is when the document is given a number and filed/recorded in the record book. Think of the process as chain of custody going from A to B to C where everyone has to sign off on it.