I did a quick Google search of water test kits. As to what they're testing, here's a fairly typical one:
The only test of immediate interest to a backpacker (I would think) would be the "bacteria" test which I suppose could be of some value. Exactly what it would detect under what circumstances isn't detailed in the information I've seen so far.
Nothing I've read, in an admittedly quick search, indicates that giardia would be detected. I saw this on the CDC website: "Tests used to specifically identify Giardia are expensive, difficult, and usually require hundreds of gallons of water to be pumped through a filter." This was in connection with well water, but I imagine the overall principle (expensive, difficult) would apply to water in general. The CDC suggests testing for E. coli instead of giardia since the presence of E. coli is often an indicator of fecal contamination, fecal contamination being the typical means by which Giardia is introduced into water.
Therefore, perhaps those household kits that detect "bacteria" could detect E. coli which if present might indicate the strong possibility of the presence of Giardia. Maybe. I'm not really in a position to say whether or not water could be declared "safe" on the basis of one of those home kits. Anyone with science based input, please chime in here.
Any type of trip to dig into this further would be very interesting.