That non-employee spouses are allowed on company property to the extent that the CEO has to acknowledge it (and put an end to it) smacks of an unprofessional environment. Ugh.
This is an extremely odd sentiment. Now, if said spouse is causing issues that interfere with work then by all means ban this person. But as a blanket rule that seems absurd.
I don't think the fact that the CEO has acknowledged it implies anything. If the wife in question's only contact with the company was to visit to and say hi to her husband once a week, I think the CEO's statement would have been exactly the same.