I completely understand the need for certification agencies - but lets be honest here.
All the certification agency does in the OW course is scare the piss out of you about lung over expansion and getting bent. The dive tables are extremely important, but could be taught second hand, and most divers will rely on a computer anyways. Everything else is a practical skill or common sense, and of course, teaching someone not to panic.
Provided said Parent could teach said child all of the same skills that are necessary to pass OW, I honestly don't see the issue other than lack of an instructor certificate that cost bookoo bucks to obtain into the agencies pocket.
I'm CERTAINLY not advocating diving without proper training. My son will be getting certified soon, and you better believe he will go through the course just like I did.
However, at the end of the day, the basic skills to dive properly do not require formal training. You need someone who can show you how to do it, and make sure you are capable of doing it on your own.
Technical/Deep/Drift, etc, I have a completely different opinion when it comes to non-rec diving.
All I'm saying is that it would be very feasible to train someone else as long as you made sure they understood the risks of blowing off the RDP tables or ignoring their computers. The whole point of OW is to orient you with the gear and teach you basic skills while making sure you realize how badly you can be hurt by diving stupidly.
Basic diving is not rocket science, and it's really not that hard. Especially if you have two licks of sense and can read the computer and do what it says. I could have passed the PADI OW course without ever having opened the first handbook, and the in-water skills that were required to pass it were very simplistic, and easy to grasp.
AGAIN - I am not advocating un-trained divers - simply making an observation.
I would always rather dive with someone who was formally trained.
I could have probably started as a Cop with no formal training - and probably done just fine, until some of the really technical constitutional stuff popped up. IE - Deep/Enriched/Etc.
Case in point - how many places in Mexico/Bahama's can you dive without ever having your C-Card checked. I know of at least 4 off the top of my head that I had experienced first hand, even before I was certified. And NO - I never dove without being certified.