I'm late to the party here, but we just encountered this as well, and I think I might be of some help :) There are two requirements to achieve what you're looking for. The first, is that the user who is attempting to upload the new version should also have Contribute access to the project. This can be done in the Sharing menu of the project, by clicking on "View" next to the user's name, and changing it to "Contribute", if they aren't already. (I believe this will also work at the document level, but won't allow for automating the permissions in the way I will detail below). The second requirement is that the user have a proofing license that is higher than "Manager", which can be addressed in ProofHQ's setup menu as Richard mentioned. For us, the sticking point has always been the first requirement, as the second one is easily taken care of when creating a new user account. This past week, however, we finally took measures to automate the access upgrade for users who are covering other users by editing our Task behavior. In the Setup > Project Preferences > Tasks & Issues menu, you can set up your Access such that when someone is assigned a task, they automatically receive Contribute access to the project. This sounds really scary in terms of giving standard users too much power, but you can configure it to be fairly harmless by clicking on the Contribute dropdown and unchecking any features you would rather not give by default (I've attached an example screenshot here, hopefully it loads properly!).
Mike Perez