Sounds like a case of a programme editor asking asking for someone to clip up a bit of SOT of Boris from the debate and a producer doing what they'd do for any other SOT
And is routinely done (for all parties) during PMQs and other activities in the House of Commons chamber.
There's strict rules about what you can do with footage from Parliament, so it becomes a grey area. Yes they cut out a part to make it fit, however it's been edited down - which you're not allowed to do and you could argue both sides I suppose.
Usually in TV, there's clips used with VO around it to help cover that rule.
2 Editing the material
2.1 You may not do any of the following:
(a) edit, alter, add to, distort, or digitally manipulate the material in any way, except to select and reproduce excerpts from it or to make colour corrections; or
(b) reproduce the image or sound out of context.