This should be fixed now. Long story short, the uploader uses an authentication method that is based on the account you're signed in with, and it has to verify your account on each file uploaded. This makes sure that other people cannot upload files to your account.
Turns out that one of the things we check to verify your account credentials was being calculated differently depending on where you clicked the "Upload Files" button. It sounds complicated (because security sometimes is) but nevertheless, it should be all better now.
Please test what you were doing that caused the error before and report back here to confim that everything works now.