From the article you linked.

researchers report that the substantial antidepressant effects of psilocybin-assisted therapy, given with supportive psychotherapy, may last at least a year for some patients.

So, essentially what I said. There is a difference between an anti-anxiety or anti-depressive drug and a drug that's useful in therapy to treat anxiety or depression.

Anti-depressive and anti-anxiety drugs function on their own, but only so long as the drug is active in your system. Psychedelics allow self reflection to enhance traditionally non-drug therapies. They can even lead to the exact opposite results when used in an improper mind set or setting.