I think you may have missed @Bill_II’s point here. He was pointing out that different data sets are cross-checked against each other. When two different methods of measuring something give the same value, that is a pretty strong indicator that any underlying assumptions involved are reliable.
In some cases, you can establish limits on the starting point of the rock from its chemical properties. For example, zircon crystals can accept up to about 1% uranium or thorium, but never contain more than a few parts per trillion of lead, simply because lead atoms do not fit into their crystal structure.
In other cases, you can determine the age of a rock sample without needing to know anything about its original composition using a more advanced technique called isochron dating. This works by taking several different samples from a rock and plotting a graph of, for example, 87Rb/86Sr against 87Sr/86Sr. The maths is a little bit more complex but you can determine the age from the slope of the graph without needing to know anything about the original composition of your sample.
They greatly exaggerate the extent and significance of these bad dates.
It’s important to realise that there’s a vast difference between “doesn’t always work” and “never works.” What YECs don’t tell you is that these erroneous results are very much the exception rather than the rule, accounting for at most 5-10% of radiometric data overall. They also tend to imply that because dating method A doesn’t work on rock type X, that means that dating methods B, C and D don’t work on rock types Y or Z either. That simply doesn’t follow.
The fact remains that 90-95% of the time, different radiometric techniques give exactly the same results as each other within error bars. This simply wouldn’t happen if these techniques never worked, and certainly not if they were so out of whack that they consistently failed to tell the difference between thousands and billions.
Ah, the good old “fossils are used to date rocks and rocks are used to date fossils” shenanigan. An over-simplified and thoroughly dishonest straw man caricature of stratigraphy that bears no resemblance whatsoever to what real scientists actually do, and that completely misrepresents what constitutes circular reasoning and what doesn’t into the bargain.
Circular reasoning would be fossil A being used to date rock B and rock B then being used to date fossil A without any reference to any other form of evidence. What happens in reality is that rocks A, B, C, D and E (whose ages have been determined using radiometric and other techniques) are used to date fossils F, G, H, I and J of the same species, and then another fossil K of the same species is used to date rock L. Typically, the result is then cross-checked further using other index fossils, or other independent lines of evidence. That is not circular reasoning; it is inductive reasoning.
(For anyone who’s into graph theory, the lines of evidence do not form a circle; on the contrary, they form a directed acyclic graph.)