The courts have to have established the scope of the word "intentionally" in "intentionally access without authorization". The narrow reading is "intentionally access" meaning that the state does not have to establish intent with respect to authorization. The first step therefore is to determine exactly what law is applicable. 18 USC 2701 refers to one who
intentionally accesses without authorization a facility
intentionally exceeds an authorization to access that facility
18 USC 1030 says:
(a)(1) knowingly accessed a computer without authorization or
exceeding authorized access...
(2) Intentionally accesses a computer without authorization or exceeds
(3) intentionally, without authorization to access
See US v. Yermian for analogous discussion of "knowingly and willfully" in the false statement law 18 USC 1001
whoever, in any matter within the jurisdiction of the executive,
legislative, or judicial branch of the Government of the United
States, knowingly and willfully...
(where the issue is whether a person must know that the false statement is in a matter within federal jurisdiction).
The prosecutor is not allowed to argue what the law says, nor is the defense allowed to make such an argument. The practical tool for translating statutory language to human-decidable question is the jury instruction. There is no single jury instruction for all federal computer access laws. The Dept. of Justice has some draft jury instructions here starting p. 157, with no explanation of their authority. In the particular circuit, there may be an instruction which eliminates ambiguity, if it exists in the statutory language. If so, the judge will read that instruction. However, the judge is not allowed to make stuff up if the pattern instructions are not clear enough (or don't exist on the particular point).