Colin Powell is famous for violating the [Colin] Powell Doctrine. That’s pretty much the definition of not having your integrity intact.
Here’s a Q&A with Washington Post columnist David Brodeur that talks about it.
Here’s something by former Regan aide Edwin Meese
And here’s one about a former NBC News executive that touches on it as well.
Consensus: it was discussed but not genuinely offered.
As I heard it, Colin Powell’s family talked him out of running, primarily because his wife had undergone treatment for depression, and they feared (not unreasonably) her problems would become a major campaign issue.