More than likely its a fitting problem. However some horses do have offset mouths. Meaning they don't line up just right. You can see this with thier teeth and how they are set within the mouth itself. (esp with under or over bites) and yes some do have jaws offset to the left or the right (teeth will also show that evidence). "Wrynose" aka "wrymouth" aka "wrymuzzle" is another problem but one can definitely see that problem with out much probing. The entire muzzle is offset to one side or the other. Its not that common though.
Some horses like to carry a bit to one side or the other so they situate it to where they like it in the mouth. Some do it as a way to evade commands, some do it due to pain, some do it because they don't know any better, (like a youngster being bittted for the first time and etc)some do it because that's just the way they like to have it set in the mouth. So there are a variety of reasons.
I too would like to see pics when you get them.
"The question is not, can they reason? nor, can they talk? but, can they suffer?" Jeremy Bentham