It isn't true. It isn't true for the San mai III mostly because the convex edge robs it of a lot of wood chopping performance, and the edge is also too thick. The Bk-9 outperforms the Trailmaster slightly in wood, even the V-edged Trailmasters.
The Trailmaster blade is too narrow to really have unbeatable geometry, but it could be hard to beat with a true flat grind on top of a really thin edge. The convex grind "fattens" the blade and robs performance in chopping wood, but that is simply true of all convexed knives: My Fallkniven Odin had the same issue. The performance of convex edges is largely the result of them being thinner than the V-edges they are compared to...: At "equal" 0.020" edge thinness, depending on how you measure the convexing (which edge thinness so far only Randall, and a few Al Mars, make as true V-edges on a proper hollow grind), the V-edge and hollow grind combine to be inherently superior by a wide margin.
Want real-world proof? How about this chopping comparison I made between a slim, very pointy, 11 ounces 7.75" Al Mar "Special Warfare", and the burly 17 ounces 9.5" Trailmaster: The hollow grind and V-edge of the Al Mar allowed it to be a rough match after 20 chops: The Al Mar's performance felt incredible, while the Trailmaster you could tell was being "held back" by its brand-new convex edge... The Cold Steel now does significantly better with a sort of partial V-edge worked into the convex, but its blade is on the narrow side for real chopping performance: I expect the Randall Model 12, with its deep hollow grind and slightly "flaring" blade, will prove better, despite being only 0.22" thick vs 0.30" for the Trailmaster...
One thing to note with the Trailmaster is that the handle felt too narrow to bear the impacts of chopping confortably. The checkering felt too aggressive also, and I do not say this easily as I did not find this to be true at all on the Chris Reeves Jereboam's aggressive metal knurling, which was the best handle I've tried so far (especially against the vibration prone Bk-9)... Form-fitting handles are not necessarily the best either, since the top of the handle is always narrower, where the broadest support is needed... Handles that get closer to round are more confortable for chopping, but have more of a rolling tendency when the blade slips into the wood's grain, which is a bit unsettling...
Gaston