There is virtually no 14C in rocks more than a few hundreds of thousands of years old as 14C is radioactive with a half-life of only about 5,730 years. There is negligible 14C in fossil fuels (such as coal) for a start, which directly contradicts any claim that the 14C is the same in all strata.
Addendum: While the article linked in the question states that 14C is found in fossil fuels and rock strata, it is notable that there is no evidence or citation provided allowing this to be verified. There are however papers that would support this claim, for instance this one
Baumgardner, John R., et al. "Measurable 14C in fossilized organic materials: confirming the young earth creation-flood model." Proceedings of the fifth international conference on creationism. Vol. 2. Creation Science Fellowship, Pittsburgh, PA, 2003. (pdf)
However, I wouldn't regard this as being a peer-reviewed scientific conference. If it were published in a regular scientific journal it would be rather different.
Note also that (as pointed out by @DavePhD in the comments below), small amounts of 14C may be formed in some rock strata by other mechanisms.