I spoke with a very patient and helpful person from TPSL today and feel a lot smarter than I did before!
I wanted to jot down something before I forget:
TPSL uses a CO2 test to determine the available nutrients in the soil. The test mimics what plants roots do in the soil to get nutrients. The results of the test are realistic in terms of what plant roots find in the soil.
Most (almost all?) other soil labs use a strong acid to extract nutrients from your soil sample. It extracts everything, regardless if plant roots would be able to extract them or not. They then adjust their numbers based on what type of soil you have to arrive back at the levels that are meaningful.