The CFAA requires you to have "knowingly (accessed a computer without authorization or exceeding authorized access)." (Under typical statutory construction rules, the mens rea requirement should distribute as shown by the parens; I have not checked whether case law has construed the CFAA specifically that way).

If you had permission to access the website otherwise, and exceeded authorized access because of a bug, you would not have met the "knowing" requirement and would not have violated the CFAA.