John did work for Randy Sparks around that time, but never as a member of The New Christy Minstrels, the group founded by Sparks.
Randy gave young Henry John Deutschendorf Jr., his first job, performing at Sparks' folk music nightclub, Ledbetter's, in West Los Angeles. John showed up for an audition still carrying his luggage, having just arrived in L.A. from college in Texas. "Little Johnny Deutschendorf" was too long a name to fit on the marquee, so Randy looked around his office and saw, in a frame above his desk, the sheet music from a song he wrote, called "Denver". He told the sign painter to put "John Denver" on the marquee. John protested, saying it would confuse him with actor Bob Denver. Randy convinced him otherwise, and reminded him that since the initials were the same, he wouldn't have to buy new luggage.
Randy arranged for John's first studio recording -- four songs; three of Randy's compositions, plus Ian & Sylvia's "Four Strong Winds". I have a copy of that vinyl pressing here in my office.
If you don't believe this story, you can ask John's uncle, Dave Deutschendorf, who today works for Randy Sparks and performs in concert around the country as a member of The New Christy Minstrels.