The recording was from the original trio -- Chad Mitchell, Mike Kobluk and Joe Frazier (no, not the boxer...) -- and the way one can tell is by the name. After Chad left, so too did his first name, and the group became just "The Mitchell Trio." A while back, I posted a video here of the Mitchell Trio when John Denver was with them.
(Interestingly, Denver stuck with the group even after the other two members of the trio left, For contractual reasons, though, they couldn't call themselves even the Mitchell Trio, and performed as "Denver, Boise and Johnson." Side Note: the "Johnson" part was Mike Johnson, who eventually had his own solo career, including the hit, "Bluer Than Blue." They all finally disbanded in the late-60s. And John Denver did just fine.)
By the way, not to get even more confusing, but for the sake of accuracy, when people refer to the "original" members of the Chad Mitchell Trio, that's not completely accurate. A fellow named Mike Pugh was in the original group, but he left after a couple of years to go back to college. That's when Joe Frazier entered, and it was after this that the group became established, started to rise, and hit its stride and fame. However I'm pretty certain that Pugh was with the trio when they were backup performers for Harry Belafonte, and sang on his famous Carnegie Hall album in 1960. Pugh left soon after, and Frazier came in. And the group, as most people know them, began touring on its own.
Several years back, in 1987, there was a PBS special which reunited these three main original members of the Chad Mitchell Trio -- and they even brought back John Denver. And near the end of the show, all four performers sang together for the first time. I thought it might be fun to take a look at that. And so we shall...
(That's Chad Mitchell to John Denver's left. The other two members are Mike Kobluk and Joe Frazier. And sorry, no, I don't know which below is Mr. Kobluk or Mr. Frazier. I think Joe Kobluk is the one of the far left.)