Actually 60 minutes HAS run almost complete repeats, but unfortunately they usually call it something else in those cases, and have a new wraparound at the very beginning.. They did a "very special ladies" one within the past year or so, which was just rerun episodes.
So technically, no I don't think they do COMPLETE reruns. But, as I've described before, listen to the intro and if they say "As we first told you last March" or something like that, you can skip it, except VERY rarely they put on a tiny bit more explanation at the very END of the story (followup).
Worse examples though:
(*) "48 Hours Mystery" seems to rerun A LOT, but it virtually if not 100% always has a new original air date, when they HAVEN'T updated it. (There *have* been some updated versions of shows too.)
(*) "What would You Do?" seems to never mark their reruns as full reruns.. ONCE in a while when they do a "2 new and one rerun" segment, then that one segment will have an "Originally aired X/Y/Z" overlay.. But they rerun complete episodes, yet don't make it clear when they're reruns.
Both of them, I've watched part of an episode only to realize I've seen it. (I have since kept track of 48 hours mystery.. and *think* I tend to remember if I've seen the latter.)