This multiple views thing will take some getting used to 
(I'm new to fritzing and haven't used it a lot yet), I was looking at the schematic view (which as you note was incorrect) and didn't think to check the breadboard view to see actual physical wiring. In addition with the wires physically connected as shown in the breadboard view you are correct it should work even though as old_gray noted fritzing doesn't think they are correctly connected (yet another source of confusion).
Looks pretty much like you are good to go and now its only a small matter of software
Peter Van Epp