OK, after living with this for a lot longer, let me put it a different way.
The widget is called "Last Seen Assets." This, to me, strongly implies that the date visible directly in the widget should always reflect when it was last seen.
It does not always reflect that.
When a PC can actually be seen, like in the case when it's on, it does.
But, otherwise, perhaps when the PC is off or even gone, the date reflects *Last TRIED* instead, and that's not good, since the at-a-glance nature of the widget is ruined. Just glancing at it, you have no idea what's real and what isn't. This problem can be verified by hovering over an off/absent machine name and noting the date and time in red there--labeled Last Tried--is an exact match for what's showing directly in the widget. The widget that's called Last Seen Assets.