I am in InDesign CS6, on a 2011 iMac, and I am often seeing this problem when I try to fit a text frame to its contents.
At first it looks like this:
Then I either click "fit frame to content" in the Object menu, or by double-clicking the lower-right handle of the text box.
And then I get this thing:
The font is Montserrat (free font, you can install it and see what this does on your end).
The fitting is perfect on left and right and on the bottom, but there is a 10 pixels margin between the top of the text and the text box.
This is really annoying when I try to align text boxes with objects horizontally, because I then have to create outlines for the text boxes.
Since this doesn't always happen, only with certain fonts, I am led to think that the height of the letters isn't properly calculated inside the font file? I am going to ask the developer of the font for help as well, unless there is something like a hidden default top indentation value that I'm not aware of, or a workaround that someone will kindly point out.