In the past few years art material manufacturers (Liquitex, Winsor-Newton, Holbien, etc.) have been coming out with oil paints that can be thinned either mineral spirits or with water. I checked the labels and they all have “traditional pigments mixed with modified linseed oil”. Now any wingnut knows oil and water don’t mix, so How the heck does this work? Also, do you think that mixing oil paint with water will speed the oil paints “drying” time (cuz’ I assume we all know that oil paints dry by oxidation, that is to say by grabbing oxagen out of the air, right?) or is the big “O” in “H2O” too well bonded.
I don’t know about the modified linseed oil, but your doubts about oxygenation from H2O are correct. The reason there’s so much water around is because it is so stable. If it oxidized things it wouldn’t be much use in firefighting, for example.
Just a WAG, but maybe the linseed oil is emulsified and mixed with water.
“non sunt multiplicanda entia praeter necessitatem”
– William of Ockham
Paints dry by water evaporating (latex), solvent eparoating, curing. There is some chemistry going on, but NO oxidation.
And the prize for best creative spelling of “evaporating” (after first getting it right) goes to …
… sunbear!!
But you’re right. You wouldn’t want your paint to oxidize.
“non sunt multiplicanda entia praeter necessitatem”
– William of Ockham
Sunbear is right (even if his typing is a little erratic 
).
Oils are made of long-chain molecules. Oil paints ‘dry’ by forming chemical bonds cross-linking the chains. (Some kinds of oil don’t cross-link, so they stay liquid.) A similar (but extreme) case is pine gum; it starts as a thick, sticky liquid, but ends up after a few thousand years of cross-linking as amber.
After spending some hours with an art conservation specialist, I would suggest that you don’t use anything with a linseed oil base in your artwork unless you really hate IT, the subject, or the purchaser. Linseed oil will pick up every dust and lint molecule from today until the artwork dissolves. If you turn into the next Van Gogh, and we have to re-claim your ear, you might end up being Mickey Mouse. (depending on the restoration specialist.) [Food for thought…pass on the linseed.]
“There will always be somebody who’s never read a book who’ll know twice what you know.” - D.Duchovny