Re: Horses and sword guards (tsuba) on the Japanese sword
Often the sides of the nakago-ana (the hole in the tsuba you're talking about for lurkers) isn't in tight contact with the blade surfaces. This is especially true with tsuba fit with seki-gane (the metal plugs at the edge and back). This used to have full copper seki-gane on both top and bottom as they'd be hammered those dimpled areas on the edge and back sides. Those would be carefully filed to create a tight fit at the very edge of the nakago and back with the harder iron not coming into contact with the blade itself. So it might have been touching on one side for whatever reason and the fitter made an adjustment.
I'll also point out that regardless swords are often a lot less symmetrical than they should be. You think it's fairly symmetrical until you look at parts fit to it closely. The shinogi may run lower on one side or the shinogi ji may slope a bit more on the other... but that's probably not the case here but simply repeated fittings and the use of seki-gane.