Note also that the coral in the photo is a rugosan coral. Coral reefs around the world were made by totally different kinds of corals before the Permo-Triassic extinction. No reef could form during a violent global flood of the sort imagined by modern flood geology (as Kurt Wise has admitted), yet there are reefs formed by various types of organism found through most of the Phanerozoic.
On carbon-14: Trace amounts of carbon-14 may be present in diamonds (and practically anywhere else) due to radiation from the decay of nearby radioactive atoms; the amount might not be absolutely zero. But there is no evidence of meaningful amounts of carbon-14 in diamonds. Suppose I have an hourglass that takes 10 minutes for the sand to drain out, and I use that to time baking some biscuits. Two hours later, the kitchen is full of smoke but I insist that the time can’t be up because there’s one sand grain sticking to the top part of the timer. I’m not going to be very successful at suing the manufacturer of the hourglass.
Carbon-14 is in the air and in us, among other things that contact the sample. Trying to obtain a carbon date involves getting as clean a sample as possible, but you can’t prevent all contact with air. For average samples, anything beyond about 20,000 years is maxing out; extremely clean samples might be pushed to around 50-60,000 years. The amount of 14C is so low in anything that old that a trace of contamination will throw it off. The actual study makes it clear that they were testing how close to zero they could measure.
Carbon-14 dating provides excellent support for the historical accuracy of the Bible. While it demonstrates that the young-earth interpretation is wrong, it shows good archaeological matching from Abraham’s day onward. (Before Abraham, the Bible doesn’t give enough detail to have anything specific for the archaeologist to look for.) Although there’s no specific archaeological evidence of Abe himself, the geopolitical and cultural setting is recognizably that of the first quarter or so of the second millennium BC. Carbon dating confirms that major building happened in Israel during the united monarchy and that Hezekiah’s tunnel dates to Hezekiah’s time. It also shows that some crank misinterpretations of the sectarian accounts in the Dead Sea Scrolls are wrong. Besides biblical texts, a variety of other writings are present. The sect looked back to their founding by the Teacher of Righteousness, who retreated into the wilderness with his followers due to opposition from the Wicked Priest. Unreasonable claims that the Wicked Priest was Paul, Jesus, or some other figure from early Christianity have gotten some pop publicity. But scrolls referring to the conflict between the two date to before 100 BC. Although exact identification is uncertain, the Wicked Priest was a figure from Seleucid to Maccabean time.
Radioactive decay rates reflect extremely fundamental physics. One type of decay happens when an electron is captured by the nucleus. Not surprisingly, the likelihood of capturing an electron is related to the likelihood of an electron getting close. In turn, as electrons are involved in chemical reactions, there is a tiny variation in the rate of electron capture decay because of the chemical setting of the atom. But electron capture decay is not used for dating. Any significant change in decay rates would make the existence of atoms impossible. You can’t just mess with a physics constant because you don’t like its implications. Decay rates occurring in distant supernovae match what we measure in the lab today. The polonium halo argument used by young-earthers requires the decay rates to be unchanged. (It also requires a lack of contamination, which is not true for the relevant rocks, and has a few other problems, but it’s an example of inconsistency in young-earth claims about decay rates.) In fission-track dating, you count the number of holes made in a crystal by the decay of radioactive atoms - no assumptions about the amount of parent and daughter isotopes.
One process that does affect the decay rate is if enough radiation is around to trigger a nuclear reaction - nuclear reactors and nuclear bombs. But for them to work properly and not have one unexpectedly turning into the other requires the underlying laws of physics to be unchanged. And we have geologically ancient nuclear reactors that show unchanged laws of physics applying to them relative to today. It’s not ancient aliens nonsense, but rather happening naturally in rocks. Near Oklo, in Gabon, uranium mining turned up isotopes similar to the output of a nuclear reactor. Enough uranium was naturally present (having had a couple billion years less decay time) to create a natural breeder reactor.
Carbon dating matches up with patterns from cycles in earth’s orbit (Milankovitch cycles), counting growth rings in trees, counting layers in glacier ice, counting lake bed layers, counting layers in cave formations, historical records, accumulated radiation effects on other minerals, rate of change in amino acid structure, and many other lines of evidence.
Answers in Genesis is merely misrepresenting the results of the experiment to fool people into mistrusting science and believing them instead. Galatians makes it clear that anyone who teaches that you need something besides the work of Jesus to save you is a false teacher. That’s a problem for people who claim that you need creation science to be saved.