This goes w/o saying.
I think the better question is what if the PM has a coherent vision and is helping engagement/metrics. Is delivering on the outcomes that leadership wants. And can do it all by 2pm?
Our culture has become so obsessed with working for the sake of working. We talk about being outcome focused, rather than just doing busy work. But when someone is actually outcome focused then we want them to stay busy.
I agree that if the person isn't delivering results then they shouldn't do the job. But if they are delivering results then why do I care what they do with their afternoons?