The system will offer the end user all possibilities on the grid regardless of the picklist constraints in place so that it does not have to load and examine every record of that type in order to determine the appropriate choices to offer on the grid. This is done to keep load times efficient.
The good news is that I think you can do what you are describing via object permissions on Standard User Team. Here's a quick example:
Hope this helps!
Of course, the object permissions, I didn't thought about that. That solved my problem