That's the OED in a nutshell: it has always looked for the printed evidence and is therefore out of its depth when dealing with the spoken language. No shame in that, but just don't expect anything else.
True that, and my professional use of the OED is mostly concerned with the 14th c., where the lag is something shocking. But for such a recent usage, in a slang which was the focus of so much favourable attention, in print, in its own time, the fact that the new breed of OED editors, who are all down with spoken language and such, can find no persuasive evidence seems pretty telling.
Two points: in the 21st c., I think the contrast with written evidence is the sort of saloon bar make-it-up-as-you-go-along that gave us "posh" as an acronym.
Second, what are the personal motivations for an OED editor? Do you get more fame and brownie points for saying "The origin is this ...", or "I don't know..."
Note that they have retreated from an earlier inclination towards the Burton ale theory.
I think their confessed ignorance is more than the product of a bias towards the written form of the language.