There's no reason to use sunscreen instead of tanning. It doesn't take a very dark tan at all to protect against burning and 97% of all skin cancer types.
It's the people who use sunscreen all the time, except one time where they end up getting burned, who are at risk of getting skin cancer (not to mention they are devoid of the vitamin d which would protect them for the DNA damage that may lead to cancer. As for melanoma (the dangerous skin cancer, but also most rare, that is caused by UVB rays) there's not much you can do about that except try to stay healthy (ie, get lots of sun and eat fat).
Also, ever notice that we have had this sunscreen propaganda pounded into our heads for the last 20 or so years, yet incidents of skin cancer keep increasing with use