I don't claim to be that great at woodworking or guitar playing, but I do both (neither one professionally). Because I do both I love guitars not only for their musical value, but as highly refined and functional woodworking pieces (I'm talking about real guitars, not the junk that gets spit off the Asian assembly lines at a rate of a couple thousand per day). Most well made guitars I've seen don't have any sort of finish on the fingerboard. They say that fine instruments only get better with use. And hand oil--not hand dirt--is, in my opinion, one of the reasons for this. If you pick up a guitar that has been used a lot for a long time, it has a feel that cannot be achieved through any process other than having fingers with their natural oils dancing up and down the fret board. It's a natural process like the smoothing of river rocks tumbling in a stream. This natural oiling process can also give some indication as to the players style. Look closely at the patterns on the finger board and you'll get some idea of where he chooses to do most of his playing. Does he stay mostly in the first position using mostly open chords or does he do a lot of soloing in the mid to high range. To me this is all part of the guitar's character and story. And if it's a fine instrument that is worth handing down to future generations, those generations should not be deprived of the story.
The only oil that get's put on the necks of my guitars is hand oil. That is, clean hand oil- not hand oil mixed with hand dirt.
For those reading that are not interested in guitars, think of an old wooden plane or the wood handles of your favorite hand tools. My uncle has some that have decades of hand oil deposits. You can't get the same feel from any comercially available finish or oil. To me it's a desirable feel that would be ruined if you tried to monkey around with it.
If there's already dirt on the finger board, I would use a rag lightly dampened with water to rub it off. The water will loosen the dirt, but won't disolve the hand oil. After the dirt is removed apply additional layers of hand oil finish by playing at every possible occasion.