Testing is hit or miss and this has been confirmed by doctors I talked to. Most labs use microscopy to detect the ova (eggs) or markers for protozoa (cysts, trophozoites).
The life cycle of parasites starts from the ova and then goes from there, the 'things' people see (visible) could be the adult stage. The one thing to look for are the tapered heads or tails*. Where tapes usually shed visible ova which appears as white rice.
*the juvenile life cycle is the stage after ova and before adult. These can be viewed under a low power microscope (10-40x) and under this magnification, you can clearly see the tapers and some have a dorsal fin appendage.
The ova are very distinct from species to species and this helps them to identify the culprit. The problem with testing is that they have a standardized list of specific ova to look for. There are thousands of potential parasites so if you are carrying one that is not listed in the standarized list then you get a false negative.