The first mistake he seems to make is that he claims DNA is random, and then he looks at exons which are not random due to being under selective pressures.
The second mistake he makes is assuming that random DNA would have equal representation of all bases. This is like saying that if dice are random that we should get as many 7's as 11's in the game of craps. Obviously, this isn't true. Random mutations can and do have biases for different types of substitutions, not to mention that chemical and physical mutations will also favor some mutations over others.
In other words, there is no expectation that random DNA in a genome will have an equal distribution of bases, even if that stretch of DNA has been undergoing neutral drift for billions of years.
™ Version 4.2
(1)