The Red River Valley above Fulton/ Clarksville / Fort Towson was not fully mapped until after the Civil War. The first regional mapping beyond the Cross Timbers past today's Colbert/Preston Bend (Bryan County, Oklahoma and Grayson County, Texas) was accomplished by Randolph B. Marcy and his Corps of Discovery, but only barely. True regional maps of the western Red River Valley actually came about from the surveyors employed by the railroads. Prior to all of this, maps were mainly based on oral descriptions and localized sketches.
These two maps, both found at the Barry Ruderman Collection, are great examples. The first is from 1855 by William McNally (I don't believe there's a relation to William Rand and Andre McNally). The river in the Cross Timbers region (Gainesville/Marietta corridor) lacks any kind of detail, including the deep bend at the Red River. Also, notice the Washington longitudes... and compare them to the longitudes used by the 1891 map by George Cram. The maps show at least one degree off (Greenwich Longitude is also noted on the map!). Further, the 1891 railroad map distinctly shows the deep bend that makes up Love County, Oklahoma.
The bend at Gainesville is nowhere to be found on this 1855 map.
As the railroads began to survey their routes, maps became much more accurate, like this 1891 map.