There is nothing at all odd about this "nugget." It is a long established policy of this country (Federal law) that you cannot do work 'off the clock.' Companies are sued for such behavior.
It might be long-established law, but the notion that people aren’t free to volunteer their services to help save their employer and their jobs strikes me as odd.
Don’t (wink, wink) “officially” work off the clock (wink, wink)
I bet if anyone obeys this command, they will be looking for a job.
Yes, and the problem doesn't arise out of those who care enough about their jobs to be willing to conduct business even without pay. It arises from those that decide to throw a surprise at their employer by keeping a notebook on all the extra hours they worked and then wanting overtime/back pay for it. If the employer doesn't make it as clear as possible, and sometimes even force people to leave, it is considered to be a tacit approval for which the employee can expect to be paid.
Another case of the dirt bags hurting the folks who are willing to do what it takes to make them and their company successful, even in hard times.