It is really not _that_ accurate. It is _somewhat_ accurate, but there are a lot of variables that make it difficult to determine if the date is right without calibration.
Actually, all radiocarbon dates now are calibrated against the tree-rings going back some 11,600 years. In the area I work I have recalibrated all previous dates with the latest calibration curves. I threw out a third of the samples in the database when I could not ascertain what was sampled. Better to throw it out than get wrong information.
The actual pattern of migration matches the flood record, because they migrated along the coasts. The flood would have left the oceans much warmer, but caused an ice age on the mainland. This left the outer edge of the continents to be habitable, because they had the water to warm them. And this matches the migration patterns of the american indians (I may be totally wrong about this -- I have no direct references but am going off of what I remember from an AiG conference last year).
If you are getting your information from AiG conferences, it would be wise to check against other sources. The primary migrations of American Indians occurred so far before the dates given for the flood that they are not even distantly related. The first migration may have been some 25,000+ years ago, through Canada, followed by a second migration down the Pacific coast in watercraft some 15,000 years ago, followed in turn by the main migration across the land bridge after the glaciers began to retreat, perhaps 12,500 years ago. After that, there is a steady increase in population and improvement in technology, with some climatic disruptions, for 10,000+ years. There is no evidence for a global flood--and it would be very easy to see in this kind of an occupation site.
There is also mtDNA continuity for 11,000 years on the west coast of North America, from Alaska to Tierra del Fuego. With the latest differentiation in Haplogroup A, experts have been able to track one of the population movements, and to establish in which direction it went.
Just FYI -- carbon dating gives a young age for all organic objects in the geologic column. Even diamonds can date under 50,000 years.
I am aware of these dates, and have read many of the papers on both sides of the issue (this is one of my specialties). When you have a laboratory that can date something back to about 40,000-50,000 years, at which point the signal gets lost in the background noise, it doesn't take much contamination to give a reading in that range. You need to use AMS dating in that range, and be very careful of contamination. Even so, ground water and natural radiation in rock and soil can give produce readings in that time frame. The dinosaur bones and diamonds dated in this time frame mean nothing.
The real question is whether calibrated dates from the last 10,000 years are accurate, and that is something that everyone but the creationists can agree on. They are quite accurate. And they show a continuous occupation of western North America during the entire time. I could show you the dates, or you could probably find many of them on line. There are a lot of professional papers posted now.
The evidence for the world-wide flood is in the paleozoic and mesozoic, not in the cenozoic which is where these artifacts are found. It is possible that the date of the flood could be pushed back a few thousand years, but there are many secular geneologies that go back to Noah which support the current date, as well as the Mayans which support the same date for the flood.
Tree-ring dating is not as accurate as many believe. It was once thought that the bristlecone pines gave accurate tree-ring dates, but Lammerts discovered evidence that they can grow many in a single year.
I personally think that historical records from multiple, independent groups should be believed over tree rings. But I guess that's where a lot of the differences between creation and evolution lie.
"There is no evidence for a global flood--and it would be very easy to see in this kind of an occupation site."
It occurred in the paleozoic and mesozoic. You are still referring to the cenozoic, much of which is considered post-flood (the exact boundary is not certain, but usually either at the mesozoic/cenozoic boundary or late cenozoic -- see http://www.trueorigin.org/cfjrgulf.asp and http://www.answersingenesis.org/home/area/magazines/tj/docs/v10n1_cainozoic.pdf)
"There is also mtDNA continuity for 11,000 years on the west coast of North America, from Alaska to Tierra del Fuego. With the latest differentiation in Haplogroup A, experts have been able to track one of the population movements, and to establish in which direction it went."
No, I agree very much that this is one continuous population.
"When you have a laboratory that can date something back to about 40,000-50,000 years, at which point the signal gets lost in the background noise, it doesn't take much contamination to give a reading in that range."
Actually, the equipment they used is accurate to 90,000 years. The background that was checked against was 70,000 years. There is no reason to discard dates at 50,000 years.
"The real question is whether calibrated dates from the last 10,000 years are accurate, and that is something that everyone but the creationists can agree on. They are quite accurate."
Actually, two points.
(1) Those dates don't call creationism into question. While creationists disagree, it is a rather minor point.
(2) Creationists aren't the only ones disagreeing.
But, as I said, it is a rather minor point. My personal take is that I'll take written history over other methods any day. The other methods must assume a history to be accurate. With the historical method, the history is written down instead of assumed. But if you disagree and have a slightly elongated timeline its really not a major issue.
I read about this recently. They traced a certain Y chromosome marker lineage along the Pacific coast which differed from that of most other Native Americans. I was surprised to learn that. Then again it is pretty amazing when you consider how all of those remote Pacific islands were colonized by early peoples using primitive watercraft.