At what point are schools fine with SSAT scores?

Agreed. Andover is around 93-94 (from what parent emails have said). Groton around 90, Lawrenceville more like 83. SPS publishes an average range (or some specific math term) of admitted students, mid 60%-mid 90%

Some of it is google-able, not all. Of course those numbers mean that there is some wiggle room below.

Also, above are from memory from when my kids were applying, I am sure they may have changed but I do think they indicate a general idea of scores.