It was a bit more than that
Just claiming ..
A lot of Missouri and Kentucky volunteers fought for the CSA
https://www.familysearch.org/wiki/en/Missouri_Civil_War_Confederate_Infantry_Units
https://www.familysearch.org/wiki/en/Kentucky_Civil_War_Confederate_Units_1st_through_14th
A few hundred buried about 500 yards north of my house at Carnton
Orphan Brigade
Kentucky was about evenly divided 60/40 union versus CSA
Missouri less so even though it’s govt was more pro CSA at first till the occupation
At the beginning of 1861 Missouri government was pretty much pro-confederate. I believe Kentucky tried to declare neutrality. Both states were represented in both the US and CS congresses and both sent lots of troops to both sides. As they say history is written by the winner, so as we look at it now, neither state ‘officially’ seceded. In Cape Girardeau Mo, there is a large Union memorial and a smaller Confederate memorial at the city courthouse. The Confederate memorial has not been defaced or torn down (yet).
I had an ancestor in Missouri who served in a Missouri Union unit. His brother was a Confederate. They didn’t face each other in the same battle (my ancestor apparently did not see any combat during his enlistment).