Tests are necessary for D1 and D2 because those players have to go through the NCAA clearinghouse and be approved to be eligible to play. SAT/ACT is part of that process. It has nothing to do with any particular school. Also, there are all kinds of technical details about what money can be given at D1 and D2 schools, that partly depends on the test scores.
D3 doesn't have any of that. Eligibility is up to the school, so is financial aid (with some NCAA rules that BishopLeftiesDad mentioned). So in theory, if the school is test optional, then no-one is required to submit tests for admission.
However, High Academic D3 admissions usually do a pre-read (where they tell the coach you are admissible) based on test scores and transcript, in the summer/early fall. Coaches recruit players who pass the pre-read. If you don't submit test scores, a school's admissions office might not be willing/able to completely do that pre-read. In that case, the coach might decide to recruit other players that he can get a clear answer about. I wonder if anyone here has experience with that? My son did have test scores, so it wasn't an issue.
I do also know that this year, many schools are dropping their testing requirements, because so many are being cancelled. So, it could be that HA athletic admissions will change the way they operate, too.