Parasite Blood Antibody Tests Are Accurate

"...lab tests are unreliable."

If stool samples are taken over more than one day and then sent to one of the more reliable labs (Great Plains and Doctor's Data are two), reasonably accurate results can be expected. But yes, it's not uncommon for bugs to be missed in visual lab tests, especially if some random local lab is used.

However, blood serum antibody tests are available for most of the more common pathogens, including for worms, protozoa, bacteria, and yeasts. Stool sample analysis has its shortcomings, but the antibody tests are quite accurate.

http://www.immuno-sci-lab.com/table_135_2003.htm
http://www.immuno-sci-lab.com/table_72_2003.htm