Yorke technically didn't lie
While he's certainly obfuscating the truth and maintaining the legend of Thursday, nothing he said was actually a lie if interpreted a certain way:
Thursday did die gallantly in battle and won honor for his regiment. The fact that it was stupid was simply omitted.
When he said, "Correct in every detail.", it was in response to the reporter's description of the painting of "Thurday's Charge". It can be interpreted that he was saying the reporter's description of the painting was correct, not that the painting was correct.
Thursday's discipline and legend did lead to more pride in the regiment and the assignment , making the men better in order to live up to the reputation.