The field relationships, as they are called, are of primary importance and all radiometric dates are evaluated against them.
For example, a geologist may examine a cutting where the rocks appear as shown in Figure 1.
It furnishes some good evidences that creationists often use.
But we won't discuss the C-14 method in this article.
There are many different kinds of radiometric dating and not all conclusions we will reach can be extrapolated to all methods used.
Also, different radiometric dating techniques independently converges with each other and with other dating techniques such as dendrochronology, layers in sediment, growth rings on corals, rhythmic layering of ice in glaciers, magnetostratigraphy, fission tracks and many other methods. There exists different versions, or isotopes of many elements.
(Aside, my dad doesn’t know how old I am, he usually misses by about two years, giving him an error of almost 5%.) Not only, is this not a ‘false assumption’. Oh and here’s a link to the Table of Contents for this set of creationist misconceptions.