Is that a correct reading of the situation, or am I missing something?
Since you ask, there are a few points with the question which makes it hard to go ahead.
[[...I was surprised to read in] The Legacy of the BBC Micro
It might be helpful to reference the source in an identifiable way. Link would be great and so do addition of ISBM, Author, year, the usual ones.
By October 1983, demand from schools had increased, with 25 per cent of the total sales coming from education, 35 per cent from home users, and 40 per cent from business users.
Does that text give any reference of those numbers?
That's a higher percentage of business users than I would've expected, but okay, fair enough.
Think of them as rather low. The BBC was a quite up to date design with exceptional speed and huge support, perfect for diverse development.
The BBC Micro had a pro forma 80-column mode, but it didn't have character cells, just bitmap, and took 20K for video memory, on a 32K machine, so it was generally best ignored.
I assume you're talking about 640x256 Mode 0. There's also Mode 3 which uses 20% less memory to provide 80 characters, so 'only' 16 KiB.
It worked quite well. And such a solution wasn't uncommon. It worked fine on an 1 MHz Apple 2, half the speed of a BBC. Sure, 32 KiB base model would have left less than 14 KiB for program and data, but then again, business use does not necessarily mean 80 characters. Sure, it's handy for text processing, but that's not a major use back then. After all, why investing like 3 times the money for an up to date electronic typewriter and still needing one for output?
Also, if the task is about text processing, then 14 KiB of RAM are quite fine to hold the software and text - if that software isn't already in ROM. The BBC had a quite nice management system for add on ROMs, thus it was common to deliver ROM based applications, including text processors - Wordwise being the first coming to mind. So plenty room for 80 characters and text (*1).
More general, while a large screen is nice, it's in no way a must for business applications. Nether for inventory management nor payroll or taxes.
Maybe even more important, while the basic BBC is a great machine, it would need quite some add on for professional use, like floppies, and especially memory expansions. Not much different from Apple II in professional use at the same time. Having 128 KiB Saturn was mandatory.
And that's a point where the BBC excels over most (home computer based) solutions back then: Adding a second 6502. That not only increased speed even further to 3 MHz, but 64 KiB of RAM exclusive usable for program and data. The base unit doing all I/O, floppy and screen, while the second CPU was all for application use (*2).
(I've heard it was present to comply with a NATO directive that computers paid for by governments, should have 80-column capability.)
That's utter nonsense. NATO is an system to organize common defence by coordinating. It has no power to issue directive for government actions - or why do you think the UK is still doing their own tank design, France inkompatible fighters and so on?
So how much less can such a club influence decisions way outside it's scope?
At the same time, it has been said that US business customers were very insistent on 80 columns as the standard.
Did they, or is that just assumed?
That would seem to suggest a transatlantic difference, with UK customers more tolerant of 40 columns than their US counterparts.
I wouldn't dare to go even near making such a global statement.
80 chars are nice, but not generally needed required.
(Why? Lack of affordable alternatives, is the most obvious explanation, but by the beginning of the 80s, Commodore was offering the 8032, with 80x25 character cells and 32K RAM.)
Take a step back and look what a business application is ... yes, it's at foremost an application. It's all about software and way less about hardware. And that's why the BBC ruled. People write applications for machines that are out there, and in England it was the BBC. It's a self supporting cycle. Businesses will buy the computer they need to run the application they want.
*1 - While putting applications in ROM is still well known with the BBC, it was quite common with other machines as well. I have several Commodore 4/8xxx with build in ROMs for text processing, database handling or spreadsheets. Even more necessary whit hose, as they could not expand past 32 KiB RAM (8096 is a different beast).
*2 - A concept that was quite successful explored by quite successful with business machines like the Fujitsu's FM7/8/11 series.