One of my users was having a similar problem. Every time she opened a model, or even simply switched windows between models, the file name in the menu bar would hae the asterisk, indicating a file save was necessary.
Turns out that, even though her Task Pane was collapsed, the Custom Properties tab was "active." You can see just a slight difference in the background color of the active tab. Once she switched to a different tab, the problem went away....