Not at all true.
PADI was created out of NAUI in 1965. NAUI was going through one of its all-too-regular financial problems at the time, and they decided to withdraw from the national market and focus in California, When they made that decision, they canceled a major instructor training program scheduled to be held in Chicago. The Chicago branch of NAUI then created a new program--PADI. Its OW training program was pretty much the same as NAUI's at that point.
Soon after that, the Los Angeles County program, feeling that too many divers were dropping out soon after certification, decided to add another program that would teach some more skills but mostly introduce divers to different kinds of diving in the hope that something would pique their interests. They called that new certification advanced. NAUI, which had been formed by former members of the Los Angeles program, followed suit. PADI added the Advanced program later.
The rescue programs and specialty programs were added by the different agencies one by one over the years. Each was an addition to what had previously been taught.
The YMCA program was not part of that development path. One of the important characteristics of the YMCA program was that it was really programS. Different sites were allowed to do it their own ways.
The idea that PADI took an existing encyclopedic program and broke it into small bits is one of the most persistent myths in scuba.