You forget the part where they were starving, and this is not what happened at all (there was no attempt to arrest anyone in particular but just a scuffle over one rifle with a deaf guy leading to a discharge, after most rifles have been handed over, there was no "lengthy speech" only one guy dancing around and shouting in a trance, and "robbing soldiers" was capturing weapons to shoot back, at first using knives in the melee in the gunsmoke because again they have been disarmed before they were fired upon and actually the soldiers also likely hit each other).

The guy made up his story, pulled it from his ass.

Here's one actual account (Encyclopedia Britannica):

On December 28, 1890, the 7th Cavalry, commanded by Col. James W. Forsyth, reached the Miniconjou camp near Wounded Knee Creek, located roughly 20 miles northeast of the Pine Ridge Agency. The late Gen. George Armstrong Custer had led the 7th Cavalry to its demise at the Little Bighorn less than 15 years earlier. Big Foot saw Forsyth’s scouts and informed them that he would surrender without resistance. On December 29 Forsyth convened with the Miniconjou to begin the process of weapons confiscation. He herded them into a nearby clearing, had their men form a council circle, and surrounded the circle with his cavalry. He also positioned four Hotchkiss guns on a hilltop bordering the clearing.

Forsyth was clear in his terms: the Miniconjou must surrender all their weapons. Big Foot was hesitant, but he surrendered a few guns as a token of peace. Forsyth was not satisfied and ordered a complete search of the people and their camp, where his men discovered a host of hidden weapons. The increasingly intrusive search angered some of the Miniconjou. A man named Sits Straight began to dance the Ghost Dance and attempted to rouse the other members of the band, claiming that bullets would not touch them if they donned their sacred ghost shirts. The soldiers grew tense as Sits Straight’s dance reached a frenzy. When a deaf Miniconjou named Black Coyote refused to give up his gun, the weapon accidentally went off, and the fraught situation turned violent as the 7th Cavalry opened fire. Because many of the Miniconjou had already given up their weapons, they were left defenseless. Scores of Miniconjou were shot and killed in the first few moments, among them Big Foot. Some women and children attempted to flee the scene and sought protection in a nearby ravine, but the Hotchkiss guns fired on their position at a rate of 50 2-pound (0.9-kg) shells per minute. The Miniconjou who were able to make it a little farther were cut down by the mounted soldiers. The 7th Cavalry did not discriminate.

Immediately following the massacre, Forsyth ordered the transportation of 51 wounded Miniconjou to the Pine Ridge Agency. Hundreds of Lakota who lived there fled the area in horror; some even ambushed the 7th Cavalry in retaliation, prompting Miles to dispatch more troops to the area to quell further resistance. On January 2, 1891, a band of Lakota went to the site of the massacre and rescued a few survivors from the snow. The following day the U.S. Army unceremoniously buried 146 Miniconjou in a mass grave where the Hotchkiss guns had been placed, a location today known as Cemetery Hill. Many of the corpses were naked. Modern scholars estimate that between 250 and 300 Miniconjou were killed in total, almost half of whom were women and children. At least 25 U.S. soldiers also died, many likely fallen to friendly fire.

In the mentioned aftermath ambush, they were trapped in a narrow canyon and would have been massacred in turn if the (other) cavalry didn't come to rescue. This was less then 24 hours later. They were some really poor soldiers under really bad command.