I had a flood in an apartment building 3 years ago. It came from the floor above me and filled up a bulkhead with lights over my kitchen counter. A few weeks later I cut out small samples and sent them away for testing (one of those mould test kits). They found only the mould that's always present but nothing unusual. The bulkhead was never even aired out properly.
Consider yourself lucky. I've torn out lots of drywall that grew mold just from high humidity............. Have to wonder what "only the mould that's always present" means. Since mail away test kits can't sample for volume. then that is a really amazing comment. Kind of like saying, you have mold, but our crystal ball says it's normal.
Here's the thing now you are dealing with insurance, so you do as service master suggests and basically do nothing. Now 6 months down the road you start getting this funky smell. Of course now everything is done, sealed up, and painted. You call someone in to check and they find out you have a big mold problem behind the wall. This may call for a complete gut down to the studs and remediation people and can run into thousands of dollars. Since you already signed off with the insurance co. guess who the total cost falls on. You can bet it won't be Service Master. Not worth the chance to me.