They cannot prove anything. They only provide evidence that some drug MIGHT be present, but it could be something else causing a positive test. More supporting evidence is absolutely essential. The idea that someone could be prosecuted for a false positive test is absurd.
To give just one example, a South America country (Colombia ? Peru ? I can't remember at this point) was using a test for cocaine that actually tested for ether, which is used in processing cocaine*. Now, chemically, ether (that is, diethyl ether) is not something that's likely to be distinguishable from other ethers, including things like THF and THP which are used in some commercial products, or remain present in traces because they are used to make things like plastic wrap. So the likelihood of a false positive would seem to be high. Yet when a US citizen passing through customs was carrying a "wet wipe" type of disposable wipe with a cleaning solution in a disposable, tear-open pouch, customs inspectors tore open the pouch and got a false positive for cocaine from the contents. This was taken as evidence of cocaine smuggling, and she was held by law enforcement. I don't know how long it took for her to return to the US, but I'm sure it required State Dept. intervention. At the time, the US admin. was putting strong pressure on South American countries (particularly those w/less cooperative rulers) to do more to stop the flow of drugs to the US, and this was the result.
Relying on these tests is a result of flawed logic. IF the drug you are testing for is present, THEN you will get some kind of a chemical reaction causing a color change. But the converse does not necessarily hold, in general. If you get a reaction that causes a color change it could be due to any of a whole class of chemicals that cause a similar reaction. Call "drugs present" condition A, and "color change observed" condition B. Assume we know A implies B. Then B does not necessarily imply A (the "converse" statement). Absence of A does not necessarily imply absence of B (the "inverse" statement). Only the "contrapositive" statement -- absence of B implies absence of A -- is necessarily true given "A implies B" being true.
https://en.wikipedia.org/wiki/Contraposition
https://en.wiktionary.org/wiki/contrapositive
*This is certainly true of crack ( "free base" ) cocaine. I don't know to what extent it is true of processing raw cocaine in the field, so this test may be based on a questionable assumption anyway.