"Doesn't the twelve string rely on some mistuning between the pair to give the tremelo tuning which is part of the charm of a twelve string?"

Well... sort of. But even if both strings of a pair are tuned exactly the same there is a slight time delay (milliseconds) between their vibrations which gives the 12-string effect.

Free reed instruments such as tremolo harmonicas and some accordions can be tuned 'wet' by having pairs of reeds tuned slightly diffently. But each reed only produces one note and the instrument must be precisely tuned by the maker or an expert repairer. On a guitar, you have the open string plus the(20 or more) fretted notes. The difference might be right for the open strings but would be wrong for each of the fretted notes. Also, small changes in tuning would make a huge difference. Free reed instruments are tuned at manufacture and the tuning can be re-adjusted from time to time, whereas you (should) tune your guitar practically between every song.

.. at least I think so!