If the organization has public repositories, and the ex-employee has issues/PRs in those repositories, then I think they will continue to get notifications about followups to those issues.
Involvement with private repositories is removed as soon as the organization removes the employee, or the employee removes themselves.
I think the horror stories could only happen if the individual's account has been used for generating many API keys or similar, but there are other reasons not to rely on that sort of thing.
But being part of an organization, don’t they have admin control over your account? Could delete all of your repos, reset your keys, access private repos, etc.
Even if a tiny risk, it seems silly just to bolster the GH activity graph.
No. They have control over your membership in their org and which of their repos you can access, not your repos. Note that a GitHub account can be members of multiple orgs.