The site above explains that Carbon-14 dating is based on a few assumptions, like to deduce the age of an organism by looking at the amount of Carbon-14 left in it and calculating its age based on the time it should have taken for the missing Carbon-14 to decay. However, these assumptions our wrong because the ratio of Carbon-12 to Carbon-14 in the atmosphere has not remained constant and scientists are not able to know. It also states that other radiometric dating methods have similar problems and that these dating methods should be taken with a grain of salt. Is it true that is all assumption and how can we believe these dates?
First modern carbon dating does not assume constant Carbon isotope ratios, in fact it is calibrated against known changes in atmospheric concentration, and has been since the 90's. These baselines were created using annular tree rings which of course reflect the atmospheric carbon when each ring was grown as well as ice core data. This was an issue with the earliest forms of carbon dating (and carbon dating alone) which is why they tended to have huge error bars. Using this as an argument against modern dating is like complaining that automobiles are unsafe because they lack doors or windscreens, it shows the person has not kept up with the development of the technology. Especially considering even the wiki for carbon dating addresses the issue at length, so it is likely willful ignorance.
Second dating method are checked against each other, using things like tree rings, stratigraphy, fission tracks, etc. The are also checked against multiple samples. If multiple samples from multiple dating methods arrive at similar dates that is very good evidence of accuracy.
Other radiometric dating method don't rely on ambient conditions just basic chemistry so this is a non-issue. If you want to know more about them I suggest you ask a separate question or review the several existing answered questions about them.