Just as a reminder to readers, the 100,000 Mile Club was not based on annual travel in those old days...it was based on your lifetime United miles. Keep in mind in those days and with United being a strictly Domestic U.S. airline...100,000 miles lifetime was a much harder accomplishment than today.
I was a member of the 100,000 Mile Club and later the Half Million Mile Club.
We didn't have to send in many proofs of tickets. In those days we had a phone number at the Los Angeles Sales Office where all our reservations were made either directly or forwarded via our travel agent. They kept a paper tally of our bookings. We also had these little red paper strips/forms and envelopes to mail in any ticket receipts for airport purchased tickets.
Membership in the Red Carpet Club was the big thing about those clubs. I don't think you could even pay for membership in those days. I seem to also recall it was invitation only, as obscure2k mentions.