The literal answer is that YECs "account" for no such thing. They reject the accuracy of such dates, based on an alternate interpretation of the available evidence. However, that isn't very satisfying, so let's address the question you really want to ask, which is "how do YECs account for such supposed ages?".
The short version is that there is no such thing as "radiometric dating".
Rather, there is the ability to measure relative concentrations of various radioactive isotopes. I'm not going to attempt a detailed explanation (you could try here to start), but the short version is that, based on several (sometimes unprovable, sometimes falsified) assumptions, Uniformitarian Evolutionists (UEs) claim to be able to establish the age of certain artifacts (rocks, fossils, seeds, etc.) based on ratios of certain radioactive isotopes and their byproducts.
It should also be noted that these methods often employ various self-reinforcing feedback loops based on UE assumptions (chief of which is that God does not exist). To wit, various techniques such as position of an artifact within geological strata and alternate dating methods of colocated artifacts are used to help "dial in" the dating methodology.
The critical point here, however, is that these techniques have expected results. The methods may be adjusted in order to arrive at the "correct" results, and data that does not fit UE expectations may be discarded entirely (often written off as "contamination"). Simply the way in which these dating methods have been developed ought to be sufficient to place them into question.
Another problem is consistency. Different methods used on the same artifact can give wildly different results. In fact, there is evidence of systemic discrepancies; I'll come back to this point shortly. Other issues are known and sometimes even acknowledged by UEs.
However, to really understand why YECs reject UE "dating", we need to look at the main three assumptions on which those methods rest:
- The relative proportions of radioisotopes are fixed at the time the artifact "comes into existence" (when a rock is formed in its current state, when an animal dies and begins the process of fossilization).
UEs themselves acknowledge that this assumption is problematic. YECs further point out that e.g. ¹⁴C concentrations may have been dramatically different prior to the Flood.
- The relative proportions of radioisotopes are known at the time the artifact "comes into existence".
Not only does this rely on various assumptions, it has been, in at least some instances, demonstrably falsified. Lava rocks whose formation has been observed by living humans have, for example, been "dated" as "millions of years old". Also, again, effects of the Flood offer an alternate explanation for many observations.
- The rate of radioactive decay has remained constant.
While this assumption does seem reasonable, and is even an explanation that a YEC would prefer (the YEC philosophy is to prefer non-miraculous explanations unless no other explanation seems reasonable), it is unprovable until and unless someone creates a working time machine. In fact, even non-YEC sources have shown evidence that the rate of decay is not constant and are experimenting with altering it, while some (YEC) experiments have already demonstrated that greatly accelerated decay is within the reach of not only God, but of Man. Moreover, there is evidence that the rate of decay was dramatically altered by God on at least one occasion in the past. Such evidence includes the previously mentioned systemic inconsistencies in radiometric "dating".
Really, the upshot of all this is that you should read the R.A.T.E. report, volumes I and II. These express a number of very specific problems with radiometric dating as accepted by UEs, at least some of which, TTBOMK have not been refuted plausibly. The upshot is that YECs possess a cohesive interpretation (admittedly based on Christian dogma) of the available evidence which ought to be weighed against — not simply ignored or rejected out of hand — the interpretation favored by UEs (based on athiestic dogma which UEs will often vociferously deny).
Finally, one would be remiss to not also consider that other evidence, not related to radiometric dating, can also be interpreted as indicative of an Earth that is thousands, not millions or billions, of years old. I wouldn't know where to start here, but see the links from my original version of the answer.
Now, obviously, not everyone accepts the YEC interpretation. However, the main point here isn't to argue which is right or wrong, but to answer the question of how YECs can "account for" certain evidences which are interpreted by UEs as indicating certain ages of various artifacts. Hopefully this answer can help you on a path to understanding that.
Old answer, for posterity:
As noted in a comment, I'm not entirely sure what you're asking, as your assumption seems to be faulty. However, the critical point seems to be "Christians who reject plants existing >7,000 years ago".
Well... the only such Christians I know are Young Earth Creationists, who reject anything (other than God, of course) existing more than 7,000 years ago.
Naturally, this also means they reject the claimed age of, well, anything as being more than 7,000 years. So I think the answer to your question is that they don't reconcile anything, but rather reject the validity of any dating that gives an answer of more than 7,000 years.
Here are a couple places you can start if you want to learn more about why YECs reject Uniformitarian dating: