So has bog-standard. It's even possible they were coined separately. Box-standard seems much less commonly used, but all that proves is that more people heard bog-standard, it doesn't prove origin either way.
Bog-standard just doesn’t make any sense, anyway
It might have been a clever and apposite term in the context where it was first used. The way people learn language and the way neologisms spread, most new phrases end up repeated by people who don't understand how they came to acquire their meaning. "Pushing the envelope", for example. I think that's been fading out of use this century as new terms for cutting-edge technical experimentation have emerged, but it was very common pre-millennium and most people who used it had no idea of its origin.
So has bog-standard. It's even possible they were coined separately. Box-standard seems much less commonly used, but all that proves is that more people heard bog-standard, it doesn't prove origin either way.
It might have been a clever and apposite term in the context where it was first used. The way people learn language and the way neologisms spread, most new phrases end up repeated by people who don't understand how they came to acquire their meaning. "Pushing the envelope", for example. I think that's been fading out of use this century as new terms for cutting-edge technical experimentation have emerged, but it was very common pre-millennium and most people who used it had no idea of its origin.