So it's not some "clever hack" - the law specifically allows for not paying the licence fee if you own a TV set but don't watch live TV.
From what I can tell, your account of things is accurate. On the website [0][1][2] the requirements aren't concerned at all with what equipment you own or with how it's set up, only with the act of watching or recording live television broadcasts over any technology, including over the Internet. I imagine it still wouldn't hurt to disconnect your TV from the means to show live broadcasts, for the tiny off-chance things end up in court.
I think spuz's account may have been accurate in pre-Internet days, but this seems harder to verify.
[0] https://www.tvlicensing.co.uk/check-if-you-need-one/topics/L...
[1] https://www.tvlicensing.co.uk/faqs/FAQ99
[2] https://www.tvlicensing.co.uk/about/legislation-and-policy-A...
I find the wording here fascinating. Is watching a live stream over the YouTube app on my TV 'live TV'? Is watching a UFC event on the UFC app? What about the website?
What is TV? Is a monitor? A monitor with an aerial? Video content transmitted over certain bands?
That might make me look pretty guilty, but my TV isn't connected to an antenna, and I don't watch broadcast TV.
The bar for evidence of a violation needs to be higher. It's possible to own all of the equipment without ever having violated the BBC's licensing rule.
I'd guess with more and more watching via the internet they probably have far more success catching people watch live broadcasts via IP addresses and ISP logs these days though.