There's no mistake. As with many other things our forebearing lawmakers have done, it's not always done right the first time. HSNP is no different.
I usually don't recommend wiki links but in this case they are indeed pretty accurate:
http://en.wikipedia.org/wiki/Hot_Springs_National_ParkThe term "reservation" was the only appropriate term they could think of back then, but the removal and displacement of Native Americans from FL, NC, SC, GA, AL, TN, MS, to lands west of Arkansas in what they called "Indian Territory" in the Trail Of Tears onto reservations changed the use of the word. It was not until 1921 that the term "national reservation" was was changed to reflect what the true meaning of a "national park" was and the wrong was righted.
The wiki does omit Music Mountain in the park where "Sunset Trail" is located. They are currently doing archeological work on Sunset Trail in cooperation with the National Park Service people. So far, spear points and other artifacts there and in a small settlement found on the far west end of Misic Mountain at Bull Bayou indicate the settlment dates from 7,000 to 9,000 BC. All within viewing distance of my front yard.
The National Park Service has been renovating the bathhouses on "Bathhouse Row" (The north end of Central Avenue) for almost ten years and one is now open for tourists. Anyone who brings their own empty jugs are free to take as much spring water as they wish from a public tap on the side walk in front of Bathhouse Row. Except for the trolleys being gone and the streets nicely paved, Al Capone and Babe Ruth would see little change since they frequented town in their day.
As the (by oversight) "first" national park, lawmakers did not even know how they should be admistered officially except to set aside certain areas as federal land--others as not, so HSNP is an annomoly where people other than National Park Service personnel can own land and live within the zip code (71913). They enacted more stringent rules on land use in other NP's.
It's of no note to locals to see a Hot Springs Police squad car sitting at the same red light with a National Park Service Ranger vehicle.
I live on Music Mountain.
ROX