Insurance companies are, for the most part, pragmatic, and will therefore know that people do not keep receipts for every purchase, and indeed people could have things in their houses that have been gifted or bequeathed to them and therefore no receipts are available.
What they will expect, not unreasonably in my view, is that if as part of a burglary you enter a claim for, say, a £5k ring, that you can prove that you did indeed have the ring (valuation, receipt, photos etc...). Unfortunately there's a number of dishonest people around who will think that if they have a burglary they've won the pools and enter claims for stuff the didn't own.
Everybody has TVs and so on, and insurers accept this.
I strongly suspect that there's more to the stories that you've read, because in my experience insurers do not use spurious reasons to avoid a pay out. Insurance is pretty simple really, if you have a loss, you can demonstrate the extent of your loss, and it is not excluded, then it is insured.