note: The following is my opinion and not an official statement by the Twine 2 team.
Neither the install-able release or the web-browser based release of the Twine 2 application is designed with collaboration in mind, but that doesn't mean you can't collaborate on a Twine Story it just means that you have to work a little harder to do so.
One of the major issues you have to overcome is version control of the shared Story Project (which you pointed out) and this can be solved by using Version Control software (like Git or Mercurial) combined with a Source Code Repository (like GitHub or BitBucket). There are also third-party Window Explorer plugin (like TortoiseGit or TortoiseHg) that can be installed to make using the previously mentioned VC software easier.
It is not uncommon for Developers working on a shared project to replace the Twine 2 application with one of the utilities (like TweeGo) that can be used to generate a Twine Story HTML file from TWEE based text files. Doing this allows the Developers to use a Text Editor of their choice to edit the Passages of their share project, and many Text Editors come with built-in supports for the previously mentioned VC software as well as spellcheckers.
The instructor can then view the story project stored on each group's repository and generate a Story HML file from it as required.