Is your player using Windows 8 on a laptop? Sometimes a tap on the mousepad can be construed as a right-click by Windows 8. I have found units trying to move halfway across the map because of this terrific new "feature."

There's a Civ V bug which could be causing this. When a hot seat turn is on the black screen, the game is already running in the background. Sometimes, keys can "leak" through this screen into the actual game. This means that pressing 'e' in this screen could result in that command leaking into the game itself. You could try clearing your player password to fix this (other players can't access your turns anyway, since we set all other players' passwords to untype-able characters).

As for touchpads, Windows 8 will generally register tapping with two fingers as a right click, and tapping with one as a left click. Your mileage on this feature will vary depending on the hardware and drivers of your laptop.

"This solved it, thanks." -the player who had the problem. :) Leaking keystrokes it was.

I, too, thank you for the comment about the touchpad.

I also noticed this problem on both windows and linux. The password field had lost focus and key's were 'leaking' through setting my units to auto-explore.