I do not think the ONS would fabricate data deliberately, and I think it's inappropriate to make public suggestions that they would without actual evidence from the request to look into it. Trial by Twitter is even worse than trial by media, at least the media ask for a comment first!
In terms of the data itself, I'm curious about why nobody has suggested that the other teachers might be university, further education, tutors, other education or even schoolkids incorrectly tagged by linking to schools. I'm just not sure why the assumption is that people would see a category called "primary teacher" and select "other teacher" instead.