Nib Shape Changes When Resizing Rectangles

that should be "without anything selected"

Stretch changed to 45, Angle to -90.0.

That's where the trouble is. Seems as though your default is not set right. Like I said above.
without anything selected double-click the outline color swatch down at the bottom right of the status bar. You should get a pop-up to Change Document Defaults. Leave only graphic selected and hit ok. Set the "stretch" to 100 and angle to 0. Hit ok. Now go tools/save settings as default

Alright, tried it a couple more times... It just doesn't seem to want to save the setting for some reason. Damn.

I'm pretty sure you have set outlines to scale with object by default.

Without anything selected, double click the Outline color area in Status Bar (or press F12) to open up the Outline Pen dialog.
You'll get a dialog first asking about changing the document defaults. Check "Graphics" and click OK.
In the Outline Pen dialog you'll most likely see that the "Scale with object" box is checked.
When it is, whenever you scale an object unproportionately, the outline will behave exactly the way you show in your first post.
Uncheck the box and also change "Stretch" to 100% and "Angle" to 0.0
Click OK and from now on your outlines on new objects will behave as expected, I hope.

Note: All object created when this setting was active need to be changed afterwards.
Select them, click F12, do the corrections above but don't change the width or anything else, and click OK.

That's it Ronny! Gotta be! I knew it was in there somewhere as I went through the same problem a few years back and just couldn't remember the fix. I even found a "FixOuline" macro to use at the time. You can leave "scale with object" checked as default but would have to remember to run the macro each time to fix it. Got tired of doing that and just reverted back to unchecking scale with object as default.