I think something is wrong here. I took the AB abatement test as part of my CA contractor's license and throwing it in the trash is strictly against the law.
https://www.epa.nsw.gov.au/your-environment/household-building-and-renovation/dealing-with-household-asbestos That has been the case since the '80's.
The thing that strikes me a odd is that once materials borne with lead are removed in much the same manner as AB, it can be double bagged and put in the trash.
Don't do this with AB if it can be traced back to you.
drkshdw whoever told you this is very ignorant and irresponsible.