This literally doesn't seem to add up

How tall is Nelson's column? Apparently until recently, no-one knew the answer to this question.

I realise this is hardly news, as it happened about three years ago, but it's one of the most confusing things I've ever read, I genuinely have no idea how it could be true. Apparently, before someone got up there and measured it, we'd all been massively overestimating

To quote the story:

As part of the most thorough cleaning and restoration of the world-famous monument in its 163-year history, a laser survey was carried out to establish exactly how tall it was.

And the discovery which will render countless school textbooks out of date was that it measures 169ft from street level to the top of Nelson's hat - compared to an official height of 185ft.

I'm supposed to believe that the 'official height' was out by about 16 feet? That's 10% of the actual height. I could make an estimate that's within 10% of the actual height just by holding my finger up against it and squinting. Had no-one tried measuring the thing's shadow? Or dropping something off the top to see how long it took? Or counting how many of those ring-like things there are round the outside? Or giving a barometer to the janitor?

I genuinely find this utterly implausible, but no-one in any of the newspaper stories I can find from the time seems to have questioned it. Lazy reporting? Or am I over-estimating the numeracy of the nation?