It is known that cyclic aromatic compounds (like sterols) can pass through the cell membrane layer. It is also known that cyclic aromatic compounds can bind DNA

It is known that cyclic aromatic compounds (like sterols) can pass through the cell membrane layer. It is also known that cyclic aromatic compounds can bind DNA (this is how steroid hormones work). It is also known that DNA breakage can occur when ionizing radiation strikes alkylating agents intercalcated with the DNA backbone. Honestly, it wouldn't surprise me if sunscreen has sterol-derived compounds that in the presence of ionizing radiation could cause skin damage. We hear about this stuff all the time in things like cigarette smoke, charred meat, etc. etc. That being said, the article doesn't address the incidence of cancer caused by NOT using sunscreen. Similarly, not all vaccinations are not 100% safe, but the risk you take from not having the vaccination is far greater if you didn't take it. Therefore, people will get scared off from using sunscreen from articles like this, likely increasing the incidence of skin cancer.