Studies have shown that BHT is neither mutagenic nor genotoxic, but may have some tumor promotion characteristics at high doses. Since these levels are not regularly achieved in the human diet, it looks like the general consensus is there is little to no risk of cancer, and it is also believed that the antioxidant properties of the chemical may actually be beneficial. Pubmed review.
Why would it?
I doubt it's a DNA interchalator.
It's a radical trap, so that could even make it beneficial.
Food preservatives as dietary supplements
BHT has been used for over a decade now as an anti-senescence chemical. People supplement with it in order to decrease the rate at which they age.