When a user clicks on "Add files", if their browser supports it, they may add more than one file.
When UploadWizard finishes creating all the HTML associated with new files, it should have exactly one new invisible file input covering the Add files button.
However, if multiple files have been added, then there are multiple invisible file inputs scattered across the page.
This has no impact on the user, since the bad ones don't seem to be clickable.
But it does make it difficult to write Selenium tests that manipulate HTML on the page.