Technically it does matter whether the tree is 2 years old or 1000 years old when it "stopped living". In any given year, only the outer ring of a tree is living, i.e. only exchanging with the environmental carbon reservoir it is embedded within. Thus the measured radiocarbon age of a tree depends upon which rings that you sample for radiocarbon measurement. If you sample a tree that is only two years old (or indeed part of a tree such as a twig that has only grown for two years), then depending upon your research question (such as when did the tree last grow), your answer could be more accurate than dating any random two consecutive rings from a 1000 year old tree.
In actual fact, the age range quoted by a radiocarbon lab after calibration is typically from a single, or repeated measurement upon the same piece of wood sample (i.e. the same tree rings), which I suspect is the case with the Dixon wood measurement. What you are alluding to where you radiocarbon date different parts of the wood to obtain a date is called a radiocarbon wiggle match. The later will give a far more precise age range, but is typically employed for specific research questions, such as what is the age of the last extant growth ring, but it does require a decent number of identifiable rings, and since multiple radiocarbon measurements are used, will be inherently more expensive to do. For example, you might date 100 rings in 10 blocks of 10 rings, and wiggle the consecutive 10 radiocarbon ages against the calibration curve to ascertain the best fit of those radiocarbon ages to find out the most probable date for the calendar date of any one of those tree rings. The nature of this method means that you can often get a precision of calendar date for any given ring as +/- 20 years, sometimes even better, depending upon the measurement method (eg Atomic Mass Spectroscopy) and the shape of the radiocarbon calibration curve at the point in question. Given that the calendar age range of the Dixon wood is of the order of a couple of centuries, it is most likely just a single radiocarbon measurement from one area of the sample, without any wiggle matching.
In this respect, and speaking hypothetically, if a tree started growing in 3500 BC and if can potentially live for over 1000 years (hypothetically lets say it can live for 2000 years) and was felled to harvest its wood from its main trunk in 2500 BC for some purpose, and later archaeologists found that wood and radiocarbon dated it, then the returned age would depend upon where from the tree the wood was harvested. The wood at the centre of the tree would return an older date than the wood on the outside of the tree. Hence why, it is of interest to ask the question "how long does a certain species of tree live for?" when obtaining a radiocarbon date. If a wood sample from a tree of a certain species typically only lives for a few centuries, and it is found in an archaeological structure and you get a a radiocarbon date 500+ years older than expected, then it leads to the question as to whether the archaeological structure is older than one thought, or whether the wood was re-purposed/reused. If the tree species can live for 1000 years and you get a date 500 years older than expected for your archaeological structure, then you it does not discount the possibility that the wood was harvested from a contemporary living tree and the sample just uses the older heartwood of that tree.
So ascertaining the lifespan of a typical tree from a certain tree species is important in archaeological investigations. Also, getting an age for wood that is older than the accepted historical construction date of an object is more probable than obtaining a date that is contemporary than the historical construction date. The reason being that the heart wood of trees tend to be more durable and harder than the outer wood of a tree (sapwood which can make up many tens of rings of the outer wood of a tree can be prone to fungal decay and rot so doe s not survive for long in certain environments, or it is chosen to be removed before being used in construction because of it not being as durable).
What this boils down to is that the calibrated radiocarbon age of the Dixon wood shows it to be much older than that of the construction date of the Pyramid. the question to be asked is; Is the pyramid Older than thought, or is it more likely that the wood was obtained from a long lived tree, or from a shorter lived tree, but the wood was re-purposed (the so-called old wood problem). Indeed, if the wood was re-purposed/recycled, then it leads to an interesting question as to how many times would wood be reused from its original harvesting?
Jonny
The path to good scholarship is paved with imagined patterns. - David M Raup