There are situations where it potentially fails -- for example, in cave deposits.
In this situation, the cave contents are younger than both the bedrock below the cave and the suspended roof above.
Geochronologists do not claim that radiometric dating is foolproof (no scientific method is), but it does work reliably for most samples.
It is these highly consistent and reliable samples, rather than the tricky ones, that have to be falsified for "young Earth" theories to have any scientific plausibility, not to mention the need to falsify huge amounts of evidence from other techniques.
Most of these principles were formally proposed by Nicolaus Steno (Niels Steensen, Danish), in 1669, although some have an even older heritage that extends as far back as the authors of the Bible.