I know less about Thorpe's interaction with Patton on the 1912 U.S. Olympic team than about his interaction with multiple future generals in an amazing game at West Point later that year, which I will dive into below. We know Thorpe trained and kept fit in the communal athlete gym/track area during the 10-day trans-Atlantic cruise to Stockholm. He and Lewis Tewanima, a Hopi long distance runner who would take silver in the 10,000m race, were both students at Carlisle Indian Industrial School and were trained by the school's football coach Pop Warner. Warner records talking to several other coaches about Thorpe's Olympic prospects and training style, and the interactions make it appear the U.S. athletes and coaches were watching each other, and interacting regularly. I can't find any references to Patton and Thorpe directly interacting, but given the small U.S. Olympic delegation, the tight quarters during travel to and from Stockholm, and Thorpe's amazing victories, they presumably crossed paths at some point.
We know much more about Thorpe, and the Carlisle Indian Industrial School football team, interaction with future WWII generals, and one future president, during the 1912 football season, when the Carlisle Indians demolished the cadets at West Point.
Briefly, Carlisle was the flagship Native American boarding school in the United States. These schools were originally designed to remove indigenous children from their families, and extinguish indigenous culture and languages. By 1912 the standards and conditions at Carlisle decreased significantly, and corruption permeated nearly every part of school life. Warner served as almost de facto superintendent, and used the fame/talents of his star players, like Thorpe, to promote the school and his own prowess as a football coach. He convinced Thorpe to return to school after the Olympics, in part, by scheduling games against teams like Syracuse (who the Indians lost to the prior season), Pittsburgh (coached by a member of the Olympic staff who taunted Thorpe during the Games), and West Point.
The West Point backfield in 1912 featured four future World War Two generals; three-star commander of the U.S. Second Corps Geoffrey Keyes, future major generals Leland Hobbs and Vernon Prichard, and five star general and future U.S. President Dwight Eisenhower.
Eisenhower was a small 155-pound plebe who made the team based on pure grit. He wasn't fast, but loved to hit and be hit. In the 1912 game against Carlisle he would be directly contending with Jim Thorpe, possibly the greatest athlete in U.S. history. Prior to the showdown with Carlisle the Cadets lost only one game, 6-0, to Yale.
Game day was blustery and overcast, and the narrative of Soldiers vs. Indians very much in the minds of players and journalists. Carlisle chose the game against West Point to unveil their novel double wing formation. The double wing shifted the halfbacks closer to the line of scrimmage, and allowed for more trick play options that the outsized Carlisle Indians needed in order to even Army's advantage. "The shifting, puzzling, and dazzling attack of the Carlisle Indians had the Cadets bordering on a panic," the New York Times reported.
To compensate for the chaos wrought by the Carlisle offense, Eisenhower and his fellow linebacker Charles Benedict, began double teaming Thorpe. It didn't matter. "Starting like a streak, he shot through the line, scattering tacklers to all sides of him," the Tribune reported. During one breakthrough Eisenhower and Benedict hit Thorpe at the same time, one going high and one going low. Thorpe was slow to rise, and Carlisle called a time out for him to recover. When the referee urged play to continue, the Cadet's captain said "Nell's bells, Mr. Referee, we don't stand on technicalities at West Point, give him all the time he wants." Thorpe, always deeply sensitive to patronizing behavior, took that personally. For the rest of the half, regardless of the play called, Thorpe, and the other running back Alex Arcasa, ran directly at/through Devore. Devore finally lost his temper, and was ejected when he stomped on a Carlisle player's back.
The second half was all Carlisle, and Thorpe put up his best performance as a college player. Eisenhower and Benedict tried their high/low tackle again, but Thorpe stopped short. The two Cadets crashed into each other, and the Army coaches removed them from the field. The game against Carlisle was Eisenhower's last full football game. He would sprain his knee against Tufts the following week, then re-injured the same knee in a riding accident later that year.
With a final score of 27-6 "The Indians simply outclassed the Cadets as they might be expected to outclass a prep school," wrote the New York Times. We don't know what was said, but Thorpe and Eisenhower walked the roughly half mile from the football field back to the locker room together, talking the entire way. We know Eisenhower treasured his football experiences. In later life he was quoted comparing the integrity and morale needed to lead an army to the same qualities needed to lead on the football field. We can only image how the startling defeat against Thorpe and the Carlisle Indians molded his perspective on leadership.
If you would like to learn more check out The Real All Americans by Sally Jenkins. This is a very readable pop-history introduction to the 1912 Carlisle football team, and the context for the Native American boarding schools.