Pop history has a habit of hiding who actually played on the records. Some of the best known bands of the 1960s and 70s relied on professional studio players, and the public rarely heard about it.
The word “every” needs care, because the details differ from band to band. The cases below are well documented. In each one, session musicians supplied most or all of the instrumental playing on the famous recordings named.
The Wrecking Crew and The Monkees

The Monkees were put together for a TV show in 1966. Their early records were built in the studio by producers and hired players, many of them from the Los Angeles group later called the Wrecking Crew. That includes the hit “Last Train to Clarksville.”
The band members mostly handled vocals on those first sessions. Michael Nesmith, a real songwriter and guitarist, pushed back against the arrangement. By 1967 the group was playing on its own albums, starting with Headquarters.
Session Players Behind The Byrds’ Mr. Tambourine Man

The Byrds’ 1965 debut single is a famous example. Producer Terry Melcher brought in Wrecking Crew players such as Hal Blaine on drums and Larry Knechtel on bass. Roger McGuinn was the only Byrd to play an instrument on the track, his jangling twelve string Rickenbacker.
The vocals were the band’s own. McGuinn, David Crosby and Gene Clark sang, which is a large part of why the record still sounds like The Byrds. The group played more of its own material on the album that followed.
The Beach Boys and the Pet Sounds Backing Tracks

Brian Wilson recorded the instrumental backing for much of Pet Sounds in 1966 with Wrecking Crew musicians. These included drummer Hal Blaine and bassist Carol Kaye. The other Beach Boys were often on tour while the tracks were cut.
When the group returned, they added their layered vocals over the finished backing tracks. The result is still ranked among the great albums of its era. Not every part was played by outsiders, since Wilson and his bandmates did contribute on some songs.
The Partridge Family and Their Studio Band

The Partridge Family was a fictional TV family, yet their records charted for real. The music was recorded by session musicians, including members of the Wrecking Crew. David Cassidy sang lead on the hits, and Shirley Jones sang on some of the early recordings.
On screen the cast mimed to playback. Most of the actors did not play on the records. It is one of the clearest examples of a band whose public image and studio reality were separate things.
Andy White and The Beatles’ Love Me Do

At a September 1962 session, producer George Martin hired drummer Andy White. Ringo Starr was sent to the tambourine. A version of “Love Me Do” with Ringo on drums also exists, and it appeared on the original single.
The White version turned up on the debut album Please Please Me, as did “P.S. I Love You” with White on drums. The Beatles were far from a studio creation, and this was a one session decision. Still, it remains one of the best known cases of a session drummer on a Beatles record.