And after all that, I discovered yesterday, I learned that the PCs I was testing on were the problem. It seems that they specifically could not delete or overwrite files in certain folders (we have been operating in a test environment); I created a new user for one, and it had the permissions.

My mistake was only looking at what it was doing in VFP. Once I tried to delete a file in Explorer I found the problem. Creating a new user fixed it.

Go figure.