That's not so much about being faulty, but also the possibility that some crud has fallen into the reg during the dive. An out of gas diver going for your primary probably doesn't have the presence of mind to purge the reg before cramming it into their mouth. If that reg was the one you were just breathing, it's virtually guaranteed to be working. If it was an octo tucked away or dragging behind you, it may have some debris in it that causes even more of a problem if it's then aspirated in a panicked breath. A bungeed octo is less likely to have inadvertently collected debris both because it's tucked right under your chin the entire time, and also because you, as the non-panicked, donor, should have the trained response to always purge the reg before putting it in your mouth--which an OOG diver probably won't do.
Unfortunately, I don't have statistics. I've heard plenty of reports, first-hand or otherwise, as well as that youtube clip of a regulator mouthpiece falling off, but "panicked diver grabs your primary" is what I've always believed and maybe I sought training to affirm that belief. If you feel the panic response is to grab the octo, you're probably not in the minority in the diving world, seeing how maybe 80+% of regs out there are rigged as donate-octo
Some long-hose users will actually have a yellow regulator faceplate and/or yellow long hose on their primary, to reinforce the "grab the reg out of my mouth" by making that reg the "octo color."Not everyone is going to buy into the long hose rationale, but I think you're approaching it the right way, whatever you ultimately decide. It's all about considering the problem thoughtfully, maybe trying out the long hose setup (I'm more than happy to show you how it works in person if you haven't seen it first-hand yet), and making a decision as to whether it works for you.
