No, it happens randomely.
Here are the orders affected, you can see they happen at different increments.
326
885
910
1653
1691
1717
Payment is done with Offline Credit Card Processing v1.2
And shipping is done with United States Postal Service v1.0.2
Default Store Pickup v1.0.1 & UPS 1.0.1
I don't it's strictly a user end issue since we had an order come in with one product affected and not the others.
It would be easier to do testing by taking things in and out (extensions and custom modifications) and see what's causing it, but I can't do that on a live site, so that's why I though fake bot orders on a test site would work.