Hey Forrest,
I’ve looked at the site, but find little solid and no valuable source information, more of a collection of hearsay. What I find questionable is that it is said that boiled linseed oil (which in reality is never boiled, of course) contains substances that are “treated with chemicals that make it toxic for humans”, and therefore are out of the question for use in cutting boards. In fact, the siccatives added in extremely low quantities to heated linseed oil are metals such as manganese, cobalt, zirconium, calcium and zinc. Of course, I would not drink a glassful of such oil. However, it is very questionable whether any of this is given off by drying oils that have dried (polymerized). Due to the polymerization of the drying oils, they are no longer soluble, neither in oil nor in water (unlike non-drying or mineral oils). For example, the above-mentioned Ardvos Wood Oil No. 266 contains manganese, zirconium and calcium as siccatives, but is explicitly approved for contact with food and for use in cutting boards.
In addition, the page you linked says: “Unfortunately, all fats exposed to air eventually go rancid”.
All fats? In reality, however, in the case of drying oils (which do not actually dry, but polymerize), the very oxidation, i.e., contact with air, that would otherwise cause spoilage is used to polymerize these molecules so that they are no longer available for the oxidation processes that cause spoilage.
This is also what I find deficient about the above page: it does not point out the difference between polymerizing and non-polymerizing oils. However, the transformation of liquid oil into a polymer by auto-oxidation is the crucial property for the longevity and for the non-occurrence of rancidity, which the non-polymerizing vegetable oils and the mineral oils lack: they always remain liquid, and the glycerides, which are not linked, are open to oxidation, i.e. to degradation or building chemical compounds that smell bad. That’s why I’m not surprised that they report foul odors with coconut oil.
Of course, with all oils, you can try to remove as many degradation-prone components as possible by refining and distilling, in order to try to prevent spoiling and rancing, but they won’t become a polymerizing oil by doing so.
I, being a curious person, long ago just dumped some linseed oil into a saucer and left it on the windowsill for many months. The linseed oil slowly turned into an elastic mass that at no time showed any bad smell or other negative change. Not even after years (I think I still should have that saucer of linseed oil somewhere). The only thing that has accumulated is dust 
By the way, linseed oil is not only the main component of oil paint, but also of traditional putty and of linoleum.