That's how the incident played out. Col. Sink busted Sgt. Ranney to private, and transferred Harris out of the regiment.
This incident is dramatized for the screenplay. In real life, the sergeants wrote their letters resigning their ranks and dropped them in Col. Sink's inbox. Then they spoke to Lt. Winters, who convinced them not to do it. But the word had gotten around, from the company to the others, and then to the battalion. Col. Sink caught wind of it and acted as depicted in the series. He dressed the sergeants down, transferred Harris, busted Ranney, and reassigned Sobel to the jump school. Lt. Meehan was transferred from Charlie company to command Easy, and Lt. Winters was returned to command 1st platoon (see Ambrose's "Band of Brothers", page 53).