I mentioned my concern about how the carbon got into the specimen in the first place, especially in formerly living organisms (not just layers of rock). I asked how we were able to determine if the C14 being measured was the C14 absorbed while the tree was alive or if the C14 seeped into the tree years later after it fell and was inundated with water and C14-laden air or was deposited along with other minerals in some dinosaur bone before either was petrified.
The good thing about living organisms is that the carbon that makes up the organism is all assimilated while the organism is alive. When the organism is dead, the body doesn't build any new elements, and thus all the C14 used in the body structure dates from the time the organism was alive.
Your archeologist answered that way because you do not need to specialise in C14 theory to be an archeologist, the same way you do not need to study quantum physics to operate a laser device. The fact she didn't study that aspect doesn't mean the explanation is not there (and constantly invesigated). It's better she's a good specialist in her narrow field of archeology, that being a generalist that knows a bit of everything but don't specialise enough to contribute. And to be frank, except for a small group of JW and fundamentalists, C14 datation is trivial and not something she'll ever use. The science is solid and has been confirmed by many other datation methods.
As far as the cloud cover, there's no trace of that for the period covered by C14 (up to 60000 years ago IIRC, something really really not ancient compared to the age of the earth). Some fundamentalists pick up citations of scientists that mention is for a period far more remote, and neglect to mention the period in question. Then we end up with people mislead to think that such a cloud cover would mess with C14 datation, when it doesn't because C14 isn't used for the periods concerned (hundreds of millions of years ago, if not billions). We also have records of the climate going back for the whole period of homo sapiens, thanks to south pole ice cores, other ice cores from glaciers, cores from swamps, and tree trunks.
Knowing the global temperatures, being able to check the C14 rates through multiple methods, and comparing C14 results with other datation methods independent from C14 (some have been cited) let us have a very strong confidence on C14 dates. It doesn't mean there won't be isolated cases where the C14 content has been altered, but when you collect hundreds of human remains from hundreds of different places around the world, and asides from a few isolated ones they tell you the same dates, that are consistent with other datation methods, you can't explain it away.
