Of course he is not arguing this at all. He is arguing the opposite, that the average time of the clocks is likely to give a reasonably accurate time. What you are arguing is that the broken clocks prove that the average time is invalid. What he is arguing is that the broken clocks (faster stalactite rates) are outliers, have explanations which do not deny the validity of the averages.
While the distribution of results is interesting, in that it can demonstrate the height of the bell curve and the skewing of the peak as well as the slope and extent of the deviations, it will not really change the point of the average in this case.
The previous example of the oldest tree indicating the age of the forest, is also apropos, since one tree does not make a forest… it is only one tree. In a similar way, a few huge stalagmites and stalactites do not represent the average, if they formed much quicker, and perhaps for some time before the other stalactites began to form. The real point is not that they indicate an absolute 6000 yr age, but that they call into question the radiometric methods being applied to them.
The argument that radiometric methods mostly agree with each other is a circular argument. They are chosen and used because they presumably agree, and then their agreement is used as an argument for their validity. Yet, when they cannot date known-to-be-young rock accurately, explanations about excessive argon in the lava is given as an excuse (K-Ar) method. A previous comment was made that you don’t use a truck scale to measure a leaf, which is true. But if adding a leaf gave a weight of a hundred pounds instead of no weight at all, one would question the accuracy of the scale, even though the scale typically weighs trucks of 50,000 pounds.
In the same way, a radiometric method should give a nil age, not a 350,000 to 3.5 my age for some rock formed in the last fifty years. After all, this is how measuring things presently is extrapolated to ancient rates and ages. To get the weight of a ship and its cargo, for example, the ship is not put on a scale, but the individual components are weighed, such as the grain or oil it carries, or the volume of water it displaces. If the grain cannot be accurately weighed in smaller volumes, or the weight of water is not accurate in small known quantities, then the weight of the entire ship will be inaccurate. In the same way, the radiometric method ought not to be greatly inaccurate at the lower ranges, where it is the only place it can actually be more readily verified.
In the same way, finding carbon 14 in oil or fossil wood is a problem, since it should no longer be detectable if the wood is a million years old. (not even more than 50,000 yrs old). It is no good to counter that it would still be more than 6000 yrs old, since the method itself becomes suspect, the radio ages do not correspond, and when they appear to correspond, we are left only with the feeling that they correspond by accident, in a deceiving manner.