entering the UK under a tourist visa or waiver program, you must be able to fund your stay. The tourist visas are No Work or Recourse to Public Funds. If you are funding your stay in the UK by working remotely, you are not abiding by the terms of your visa. This isn't the same as getting an emergency call out while on holiday.
How does the border agency know? They ask you a whole bunch of questions upon entering the country. So if the plan was to work remotely you'd end up lying to them. Digital Nomads calling it a grey area is often a nice way of saying "unless you tell someone the truth, you'll be fine"
If it's something you plan on doing, I'd highly recommend knowing the regulations for each country yourself and not relying on a third-party website to tell you things. That way you decide what you say to whom and what risk you take.
