Most often they are slipped in between your body and the sash/belt, then secured with attached, or unattached thongs. If there is room you can cut belt slots.
Note the thong for tying to a belt/sash. A guy could do the simple belt loop like the Sam Huston too.
How are most done?
I've seen plenty around our neck of the woods with the belt loop, we have a heavy following of Norweigen Immigrants and the loop was their style too.
Fur trade era?? couldn't tell ya I haven't seen any documentation/pictures or any in museums like a true center seam.
I have made a few center seams with a loop exactly like the Houston sheath has. The loop has to be sewn on before the seam is sewn, and when the seam gets flattened in the press plates, the lower part of the loop is squished very thin and distorted. Of course, the seam does not really need to be as flat as I normally do them.
LONEHUNTER, that looks like one my older trade knives. Maybe 2/3 years ago or more.