I am a Noobee, But the general concences is that the OOA diver will take/use your primary reg ,reguardless of what your secondary is ?( So you should have 36-40" hose) So isnt the back up(the one will end up using) what youll be comfortable with ?(which 80% of the time is either a cheap sec/oct or AIR II neither which breath that great but both work good enuf to get you to surface) and if dumps are on BC (no need to remove mouthpeice to deflate) whats the major problem/difference?
The standard OOA as tught to OW students, is that they will signal OOA and ask to share air. You will hand them your octopus which is clipped in wahtever fashion within the upside down triangle between your shoulders to your waist. He will then hold your bc while you have one hand holding his for contact. Signal OK to each other and then, make your safe slow ascent.
Others have a long hose on their primary and donate that to the OOA diver. The donor will then go on his octo for air. They then make a slow safe ascent. This is not standardly taught in OW class. It can be addressed if questioned but typical gear configuration for the newly wet student does not include a long hose like that. It can cuse issues when they have so much to learn fresh. Can be done, but isn't the norm.
Now. Quite frankly, if you train properly, you should take the donated octo, not just snatch it form the diver. BUT. There is also the people fear condition. And when stressed, many who do not continually train and update their skills, will panic and grab for the first available reg. That is usually the one in your mouth. And those people won't signal and ask nicely. You make sure you train not to panic and handle any action that may come.
There are many options out there for OOA emergencies. Quite often, people have never practiced OOA skills once they have certified. That is a shame, because skill not practiced are not done right in crunch time.
You must be clear and calm and communicate with your buddy. Even if it is an insta-buddy, you can practice it once down for clarity. Won't take but a minute and helps make sure you're on the same page.
And finally, my buddy is my extra lifeline. I am going to make sure hi/her gear is not cheap poorly-functioning crap if they are to be my buddy. Conversely, if I know that most will grab my primary, why would I buy cheap crap if that may well be the one I get stuck with in an already tense situation?