When I saw Yeager asked about that at NASM and the Indy Speedway, he mentioned being a bit abashed by the claim.
In his autobiography "Yeager" he writes: "It was not very sportsmanlike, but what the hell."
He explained that the Me-262 had slowed down to land, and he caught up with it as the jet was over the runway. The USAAF tactic was to circle where they saw a jet taking off, knowing it would be back in less than an hour flying on fumes and low on ammo, while they could loiter for hours.
In no way is this a knock on Yeager, and it was pragmatically smart to fight the right fight ... not to succumb to the opponent's sole advantage.
My dad opened the air base at Landstuhl when Yeager came in to command the F-86 wing and train the recently reactivated Luftwaffe pilots. His son Don was one of my playground friends, and we used to have lunch at each other's base housing apartments. All the parent's friends were WWII aviators, and I learned to just sit and listen their tales. Usually VERY different that what they'd tell later in print.