Martin,
There is little unanimity of opinion about this on this board. The AF will greatly darken the wood which may cover up subtle effects in the grain. The effect of just using an oil on the wood will also vary with the piece of wood and the finishing oil used. Some people like the darkening of the wood with the oil, others don't. Stains are another issue entirely. AF really isn't a stain per se, it's a chemical reaction between iron compounds and the wood. Most stains are pigmented, that is the color comes from small particles of stuff suspended in the carrier. Almost any stain can cloud the surface of the wood if not used properly. Ideally you get the colored particles down in the pores and not built up on the surface. Depending on the stain that may require thinning and any stain will require considerable wiping before it is dry to get it off the surface. Most people who have had bad problems with stains let them on too long and can't get it off the surface. Stains can also be used to change the color of the wood - make it redder, browner, yellower or whatever. If the object is to change the color aniline dyes are much more effective than stains and do not cloud the surface.
TOF likes CrO3 but not many of us use that as if not used appropriately it can turn green through time, an effect that is terrible against a light background like maple. I have no experience with it on walnut but TOF's stock look good. As he points out it is a bit of work to use it.
If I wanted a simple way to finish a walnut stock without any danger of doing something bad and that was simple to do, I would fill it with the black Constantine's filler that Jim Chambers sells and then finish it with his Oil finish. Walnut wants some filling to look good and the filler will pick out the differential pores in the grain pattern. Jim's oil finish has a bit of a reddish tint to it that works great on walnut and it while it darkens the wood a bit it doesn't make it too dark.
Most of us have many cans of stain, many bottles of dyes, fillers of various types, and many different bottles of finish around that we've experimented with over the years. I might use very different finishing techniques and compounds on different jobs depending on the wood and what I want the final finish to look like. No easy answers.
Tom