Just Chris (my first name) will do.
If there are no resources assigned to the task, then the ETC is technically 0. The 'Team' views are irrelevant to this issue (that is project resource allocations - not task resource assignments... two different things). Open for time entry against the Task does not come into this.
There is one other thing you might want to check:
- Does the PM have the rights to edit the tasks on the schedule?
I think for the community to help you it would be useful for you to gather a few screenshots of the task pages for us to see. Namely:
1. The PPM Gantt view so that we can see where the task fits in the WBS.
2. The Properties => Main => General sub-page for the Task in question
3. The Properties => Main => Constraints sub-page for the Task in question
4. The Properties => Dependencies sub-page for the Task in question (if you don't see this sub-page in the classic view of task properties, then this is the tell-tale sign that the task is a summary task at whatever level in the WBS).