cancer from sun exposure that doesn’t cause a burn that blisters or peels like you seem to be requiring. Cumulative, non-burning UV exposure causes skin cancer, especially basal and squamous cell carcinomas. So people should know to protect themselves even if they don’t feel like they’re getting seriously burned.
As far as whether anyone can get a sunburn after 2pm (or 3pm like you shifted to) I don’t care if you believe me or not. People know that’s true through their own experiences. So their own experiences will be more than enough for them to see past your anecdotal experience.
But if you like you can look up actual research on the subject. Any Google search will give you a synopsis of the consensus.
You seem so confident though, I expect you can show me some very strong research/evidence to contravene that?