What role in the project area do the members of the team have? 

I ask because the role defined in the project area is project wide and supersedes the role defined in a team area. For example if somebody has Author role at the project level, then they still have author role even if the team area membership has them as commentor role.

So typically what we do is give team leads (and project admins) author role at the project level so they can always author content but then the other members are given the default role which is typically commentor and then for each team area they are given explicit author access, so they can only author content in those assign folders. With the default Commentor role you can always comment and link any artifacts in the project.

Now if they don't explicitly have author rights at the project level, then check to see what permissions are set for the default role.

If everything is correct then I would suggest contacting tech support for further investigation because this does not sound right.