Does removing anti-skating really improve sound?

Larryi you are essentially correct except for one thing. It is the loudest passages you want to set the tonearm for as they are the hardest to track. The lighter passages are easy and a little more bias here does not matter near as much. It is the stylus following the groove that you are interested in nothing else. Fidelity will not change at all until the cantilever is way off center in the non linear zone. Very stiff cartridges, very low compliance like the Air Tight and Koetsu might sound just fine playing a string quartet without anti skate. Put on Aerosmith and they will pop right out of the groove.  
All this is the argument for tangential tonearms. I have had three of them and can guarantee they are way more headache and unreliable than a good pivoted arm. Just ask Michael Fremer.  

I use a linear tracker (Kuzma Airline) and the fine horizontal balancing set up involves bouncing the arm while it is in its 'up' cueing position at different points along the face of a record to see which way the arm drifts-- the objective, if I recall the instructions correctly (and I re-read them when I do this setting) is drift slightly outward at rim of record, neutral at center of record and slightly inward an inner grooves. This is supposed to be more exact than any level or measure and in fact that has proven true. So the arm is level, but....
I haven't used a conventional arm for a dozen years but am adding one- it's en route to me now, and it has an anti-skate device. So, I will be doing his setting for the first time in a long time.
Riddle me this- using a test record, are you checking for anti-skate at more than one place on the record? If not, why not? (Not a trick question and no hidden agenda other than my curiosity and fairly long lack of hands on experience in messing with an anti-skate setting). 

mijostyn

Fortunately distortion is easy to hear because it is so dissonant, sort of like looking for an elephant in a garage full of cars.

That is completely mistaken. Some distortion is not all "dissonant," but just the opposite: it’s euphonic.

I am an MD and can guarantee you I know a lot more about the brain than you do. You are not your brain.

Beware the audio guru.

mijostyn,

There is a good reason for not setting anti-skating to work best for the loudest passage.  According to a number of experts, including Peter Lederman of SoundSmith, skating force varies with groove modulation, with more force at higher modulation levels.  I don't know why this would be the case, but, that is what he claims.  If you set anti-skating to be optimal for the most extreme passages, it would be too high for the vast majority of time the record plays well below that level.  Because I don't need high anti-skating to reduce distortion when playing regular records (only test records distort grossly), I go with slightly less than what is indicated by playing test records at the highest modulation level.  Lederman's observations and recommendations are base on seeing observing wear on cartridges (he is a cartridge manufacturer and rebuilder). 

I know there are all sorts of methodologies, and all of them are, at best, rough corrections, so I don't sweat it that much.

Larry, yes when the groove velocity (modulation) increases friction of the stylus in the groove increases increasing the skating force. Groove velocity also decreases as you move to the center of the record. Now, do you set your tracking force to track light passages allowing mistracking on the heavy ones chewing up the grooves? I think not. Tracking force  is set heavy enough to make it through the tough passages. Same thing goes for antiskating. You are adjusting it to minimize tracking distortion. Cleeds, please excuse me. I should have clarified myself better. I meant tracking distortion. Even order harmonic distortion can be euphoric. Pass intentionally designs a little of it into his amps. Other distortion not so, at least over 1%. Usually the bias adjustment bands are at mid disc. I guess the thought is to get an average velocity.
There are many variables you just can not account for. But, the goal is to minimize miss tracking. Any pivoted arm cartridge combination with properly adjusted anti skate is going to easily out track one without. Get a test record and prove it to yourself. If the stylus leans a little bit to one side or another makes no sonic difference. This is another reason so many of us don’t switch to a tangential tracker. There is no sonic improvement to justify the added complexity. 
Larry, Peter has no idea what the cartridges he is reduilding have been through. The owners usually have no idea.
The primary determinants of the skating force in a given arm cartridge combination are VTF and groove velocity. Modulation is a minor contributor. The geometry of the best anti skating devices is such that the counter force applied decreases automatically at the arm moves towards the center of the record compensating for the decreasing groove velocity.