This is not strictly accurate. The position does require an investigation, and the investigation is based on the SF-86, but it is NOT a cleared position. It's Public Trust, you don't get a security clearance (unless maybe if you work at ADW or JCF or something). And the security process uses a "whole-person" concept, they will take mitigating factors into account.
Now where you will run into trouble is the medical clearance. The form—again, a federal form you shouldn't lie on—asks if you have any history of "substance abuse" in the past two years, and defines "abuse" to include any use of an illegal substance, including marijuana. Kind of harsh IMO but that's what it is. The form is not the be-all-end-all, the final approval lies with the flight surgeon, but from what I understand they're a lot more cut and dry than the security people.