Origin of 'bog-standard'

Bog-standard being related to toilets/lavatories at some point is probably because of the term bog-house. In your quote from OED, it says that the use of box-standard in the meaning of "ordinary" first appeared in 1983, thus making this theory not as possible.

I have also found that 1983 quote, just for fun. This quote was said by the inventor Sir Cline Sinclair in an interview with magazine Computerworld, February 1983:

Luckily, we cannot foresee the day when a computer becomes just a standard box. There will be box-standard machines along the road, but we do not simply have to make those.

Some have also speculated that BOG is an acronym for British or German. This is plausible as during the world wars, the British and German technology was so good, that everyone had to use them, which made British or German the "ordinary". Thus, the term BoG standard was coined. Some also think that BoG is for the British or German engineering during the Victorian era. I can't find any real documents before 1970 using these terms, so this theory may be a little sketchy.

I have an answer, but can't be sure of its truthfulness though.

'bog-standard' is 'beyond-the-pale' in the sense that its outside the domain of civilised / advanced 'England', because geographically speaking, beyond the pale there were lots of bogs! In this sense bog-standard is simple or inferior, but also sufficient and rugged.

Its possible that the usage was in slang/non-standard English for a long time before being attested to.