I mainly worked with InDesign CS4 until I recently upgraded to CS6. I use "fit frame to content" for text all the time, especially when I'm trying to make a line of text a certain width so it'll align on both sides with a picture, text box, etc.
In CS4, I would create a text box to a certain width, put in a single line of text, justify the line to fill the box's width, and then "fit frame to content" to get rid of the extra text box space below the text that wasn't needed.
In CS6, when I do the same thing, once I "fit frame to content", it changes the box width back as if I hadn't justified the line to fill the box's width I wanted. This in turn means I either move the bottom of the box up to remove most of the extra space (but I can't get all of it which is annoying) or fiddle with the text size to get it precisely the width I want.
I read in another post that was slightly related to this that you can double-click the top middle handle of the text box and it'll work. But, why doesn't it work like it did before anyway? Is there a preference I should select to get it back to how it was before?
I'll have to take your word for it on CS4, but the behavior, as far as I ever knew, has always fit the frame to all 4 sides of single-line text; but only the top/bottom, (depending on vertical justificaton settings) of multi-line text. I could be wrong, but I don't believe there's a preference that affects it.
Your method of width-retention-by-justified-type is interesting, but it's a chicken/egg thing. Type justifies to the frame width; not the other way around.
If you want a text frame, (or any frame), the same width as another frame, there are many other (better?) ways to do it than relying on the length of a line of text, which is anything but constant. Set guides, turn on Smart Guides, enter (or copy/paste) the width numerically in the Transform Panel, etc.