I think that knowing frequencies and hearing frequencies still leaves one a long way from being able to tweak a string to match that frequency.

Question for piano tuners: Does tuning the piano require multiple iterations? When re-tuning my 12-string to or from an open (where some or all of the strings are tuned to a specific chord) I sometimes have to go back and tweak each string a couple times. I think this is due to the change in stress on the top and neck of the guitar.