There are multiple ways to tell how old a fossil is, one of which is extremely, pin-point accurate to almost the exact year, if not the exact year itself. It does involve which layer of earth it's in, which is a radiometric test.
Also, there are a vast amount of different tests with multiple styles and types of radiometric dating and ways we know how old the earth is, and it has very little to do with fossils. It has to do with clocks and timers we use regarding the decay of substances within materials in the Earth. Whomever told you Earth's age is based on fossils needs to get their face into a science book and out of the bible fiction.
We use this information on the age of the Earth and these tests to determine the age of things, including Fossils, which are pin-point accurate, many of which are millions of years old. As the great Lewis Black once said, take a Fossil, show it to a Christian, if they don't get it - throw it over their head.
I mean i could use the same argument against an evolutionist theory on how old the Earth is. If the Moon moves away from the Earth 2 to 3 inches every year, which if you use the same carbon dating principles they use for fossils, you assume it has been doing the same thing since "the beginning of time", which if the earth is 20 billion years old, it simply wouldn't add up. When they say these fossils existed (4 billion years ago is as far as they have dated back), the tides would have been so strong the earth would have been inhabitable. Same rule can be applied to the sun who's is getting 5 inches smaller every hour, which if the Earth is 20 billion years old, it would have not been inhabitable. But if you believe the Earth is 6-10 thousand years old, as a creationist does, then those factors would not make a unlivable effect.
We are obviously violating the threads rules but I'd like to make it clear that though my faith is in creation and not evolution i do acknowledge the fact that either way you have to believe that either God came from nothing and has always existed or that mass/energy has always existed and came from nothing. You can not argue the quantum theory against a creationist because any "law" such as it or gravity would have been put into existence by a creator that created the world. If you are interested in learning about creationism and the FACTS (That don't rely on the Bible) I can show you some videos that are highly extensive and argue all points of creation vs evolution.