I’m not sure–my Googling of the issue isn’t providing concrete evidence one way or the other–but it’s awfully hard for me to believe that that’s true. After all, there’s a $19.8 billion industry surrounding its opposite: skin whitening.
Either evolution has badly messed things up, giving hundreds of millions of humans precisely the wrong skin color, or humans are just kind of goofy.
But let’s be honest: Even if I did find concrete evidence that tanning doesn’t make you more attractive you wouldn’t care. You’re buying the feeling of attractiveness, not attractiveness itself. And simply feeling more attractive might make you act in a more attractive way.
So yes, tanning probably makes you more attractive, but it’s not the least bit clear that it has anything to do with the color of your skin.
In conclusion: If basal cell carcinoma seems like a good trade-off for a feeling, I say go for it.