The vast majority of fortune 500’s have legal frameworks up for dealing with internal AI use already because the reality is employees are going to use it regardless of internal policy. Assuming every employee will act in good faith just because a blanket AI ban is in place is extremely optimistic at best, and isn’t a good substitute for actual understanding.
Internal policies at these companies are rarely subject to a level of faith that you're implying. Instead external access to systems is logged, internal systems are often sandboxed or otherwise constrained in how you interact with them, and anything that looks like exfiltration sets off enough alarms to have your manager talking to you that same day, if not that same hour.