Wait, on my MBP/Retina;
pressing "F" in Library produces picture only. I key does nothing
shift/command/F (no control Wayne) produces "Full Screen" and most certainly will toggle info with the "I" key.. consistently
A habit of many who teach regularly (i teach the Lightroom classes here at my store) is to say or write “command/control” as a modifier, the first being for Mac users, the second for windows users. My reference was not to use both command and control, thus the / in the sentence. Often you will see option/alt used the same way.
Just some observations between the difference between Lightrooms full screen view (or mode) if you want to call it that, and Lightrooms Full Screen
Preview. Shift -Command/control F is full screen view or mode, and autohides all panels and the menu bar and zooms the working space to fill the screen. (as mentioned, this is a shortcut to hitting command/control F twice). Since this is the working space, the filter bar at the top and toolbar at bottom remain visible if open, but can be hidden (T and \). Many keyboard shortcuts still work, for example you can use the , and . key to cycle through the basic panel and the = and - keys to adjust the currently active one (and the i key to toggle through the overlay). As you do this Lightroom pops up a brief dialog on top of the image to let you know which adjustment is currently active, and each time you make an adjustment it pops up the current value of that setting.
Full screen preview is a new function in LR5, which was to replace the need to do multiple keystrokes to get a full screen image with lights out that was required in preview versions. It sort of does a full screen and lights out thing but it is working a little differently, the image is slightly larger because the space for the little autohide triangles are gone and panels are not available. - as might be expected if it’s purpose is to toggle in and out of a quick preview. In full screen preview mode, most keystrokes are still available but there is a slight difference. If you move through the basic panel or make changes to a setting, the text alert appears in the bottom left corner of the screen, not in black box in the middle about 25% from the bottom (which is on top of the image) like it does if you are in full screen view or mode. And as noted, the info overlay cannot be seen in full screen preview (on a mac). So there is some effort to not interfere with the view of the image when in full screen preview mode and either the Mac team interpreted it slightly differently than the windows team, or one version has a bug.
You can get very close to what the OP was talking about. If you hit full screen view (shift command F), hide the toolbar (T), hide the filter bar (\), then right click on the background and set it to black, full screen view looks almost identical to full screen preview, with the exception that the info overlay is now visible. Whether it’s worth all those keystrokes or not (and the background remains black when you move from full screen view) is of course the tradeoff.