Brian, this is precisely what is happening to my wife. I sent an email to the support ninjas yesterday ("[OG #434573] Problem with duplicated projects & actions").
She's not double clicking. She's not checking actions off on 2 clients before syncing.
Is it possible that you've got a bug?
My experience in a past life doing computer support at a university was that people may do things without being aware of it, especially when it comes to "microscopic" things like clicking a button, typing control-S, etc that need to be done over and over. Often, they'll insist (in good faith, I think) that they don't do those things and even express significant hostility when you produce evidence to the contrary. The experience has made me cautious about making definitive self-reporting statements like "I'm not double-clicking on any of the actions that get duplicated" if there's any possibility I could be doing it without noticing, even though my nature is to watch such things pretty closely when I'm suspicious (and I'm almost always suspicious when there's software involved!) If she's aware that double-clicking could cause this behavior and still sees it happening, that is a more reliable data point (to my eyes, at least) than asking after the duplicate actions are seen "did you accidentally double-click on any of those actions?"