As mentioned in that note from the CBP itself, it is Canada that is generally far more diligent about checking and requiring such documentation, so it would be wise to have it on hand if planning travel with minors and just one parent to/from or transiting through Canada. In the US I have only heard of rare cases of the CBP aksing a few additional questions in some cases on entry to the US. There are no exit checks by the CBP, although presumably airline staff could also ask similar questions, but I have not heard of anyone being denied travel out of the US because of this. Any pointers to actual incidents of this kind would be very useful to judge how much of a concern this really is.
As for India (since that's the focus of this forum), I don't think the Indian authorities care very much at all. It is an extremely common case for Indian families to plan their vacation travel to India with one parent (often the mother) staying longer in India and returning separately with the children. Never heard of a problem in such cases.
It's a different matter if there is litigation involved (divorce/custody cases) as court orders against travel by the minors can be enforced by immigration authorities.
To answer the original question, there is absolutely no problem with flying to India with a one-way ticket and an OCI.