When you pick the Artboard Tool, you enter a special 'artboard mode', and it modifies the behavior of standard 'object mode' commands.

For example, pressing Cmd/Ctrl + A (Select All) will select all artboards instead of objects.

But for some reason pressing Cmd/Ctrl + Shift + A (Deselect All) does not deselect all artboards, but selects them all instead.
And if I try to call it from the menu, it will deselect objects instead of artboards (if I have any object selected) or just be inactive (if I have no object selected).

This is hardly consistent and makes deselecting artboards a problem.

One can say you can deselect them by clicking empty canvas... but the problem is that accidentally clicking an object creates a new object-size artboard instead, and not seeing empty canvas in a view is a common thing, and there is just no space you can click to deselect.

...and Ai does not even change a cursor when a click is going to create a new object-size artboard! You can vote for changing it here: http://illustrator.uservoice.com/forums/333657/suggestions/47070346