Indeed, I think at least for most older people their phone is what reads on it. If it says Nokia, it's Nokia and they likely have no idea what Android/iOS/Symbian/Tizen even mean.

Right - the parent was saying if you have the absolute latest flagship phone, you're likely to know it. The type of people who don't know the model of their phone are those who aren't buying the "Just released in last 60 days and is the most expensive in it's class" type smartphones.