Text Frames don't have frameFittingOptions so therefore the generic PageItems don't either. For Rectangles you can use Rectangle.frameFittingOptions.
Thanks for the reply. What you suggested would return me an object of FrameFittingOptions. But I am looking for FitOptions. The values in both these enumerations are different. Can I get something like that?
var myFrame = app.selection;
FitOptions is an enumeration used to pass an argument to the fit method. It directs an action, it does not inspire an on-going condition. As a scripter, you could use a keyed label on any text frame for which you issued a fit command:
Now later you could examine that label to see what was last used. But this wouldn't capture a Fit command in the UI.