I wouldn't say it's a non-story exactly, and the point is not whether or not we know it's not filmed on a Sunday evening. I think the point of contention is whether the mishap genuinely warranted them being allowed to start again (like Mark and Karen's mic issues, which meant they couldn't possibly have done the dance), or whether it counted as a mistake by Fleur/Vito, in which case they should have continued and it should have been taken into account in the judging.
If the chair broke or slipped, that was a prop issue (and I wouldn't like to be the person who was supposed to have secured the chair!) and clearly beyond their control, and they were right to redo the routine.
If Fleur fell on her way to the chair, or Vito missed it or fell out of it, for me that would count as a dancing mistake.
It's a pity that (in the Mail's account anyway) the BBC person muddies the waters by talking about Fleur pulling Vito along in the prop chair when the routine didn't feature any such thing. It makes you wonder what else they're being inaccurate about.
I do wonder what would have happened had the incident happened in the main live show.
Any road up, the better dancer stayed.