Bikeman:
It doesn't have much to do with the hitch mechanism itself, but rather where that hitch connects in relation to the rear-tire contact patch. Picture it this way: You have a seatpost-mounted trailer with 100 pounds on it. You're entering a corner with the bike leaned over a bit (a bike won't turn any other way) and you are braking. The deceleration causes the weight of the trailer to push against your seatpost partially forward and partially to the side due to the angle between bike and trailer. Because your pivot point is the tire contact patch, the effect is that the trailer is trying to push your bike upright, counteracting the turn you're trying to make. This effect is very noticeable. The higher mount gives the trailer more leverage to push the bike around, lowering the mount reduces this. As a demo, sit on your bike and heave a friend push sideways against your seatpost and then against your rear axle. It should be clear that it takes much less force to change the roll angle of the bike when pushing from the post than it does from the axle.
The other problem with post-mounted trailers is that when you stand in the saddle (say to climb a hill or accelerate from a stop) the bike rolls left to right. This side-to-side motion is much greater at the seatpost than it is at the axle. As you pedal, that side-to-side motion moves the seatpost hitch around and changes the steering angle of the trailer with each pedal stroke. This is less efficient than a trailer that tracks straight and by isolating the trailer from the roll axis of the bike (something an axle-mount does) the trailers effect on the rider is reduced.
Now, none of this means that a seatpost hitch won't work. There seems to be a lot of hair-splitting on forums that gets amplified to the point where it seems that one solution is totally defunct and the other pristine. So yes, i agree that a post-mount trailer will indeed work. However, if you're looking to get a trailer that has the least effect on bike handling or if you intend to ride aggressively with heavy loads, an axle-mount trailer will be noticeably safer and better than a post-mount trailer. Google Bikes-at-work for more info on this topic and to see some cool photos of some serious bike loads (house moving, etc.)