Not quite. From your own link: „Any defect or non-conformity of goods with the contract which becomes apparent within 6 months of delivery are presumed to have existed at the time of delivery. After the expiry of this 6 month period, the burden to prove that the defect or non-conformity of goods with the contract existed on delivery generally shifts to the consumer.“
In other words: after 6 months, you have to prove that the product was defective from the start, which is very hard to do. Hence a manufacturer‘s warranty is much better than these consumer law rights. Also accidental damage is obviously the main reason to get Apple Care+, so it doesn‘t make sense to brush that aside.
For the X, I would say if you‘re generally careful with your stuff and put a case on it to protect the glass back, it‘s probably ok not to get AC+. If you tend to drop your phones or (like me) go caseless, AC+ is a very good idea and at the very least gives you peace of mind.
Well, it's often not _that_ hard to prove (if the defect was indeed present from the start). If there is no water damage, and no physical damage outside, and no sign that you (or someone else) damaged the phone, then that's a good indication that the damage was there when the phone was sold. But also, as far as I know the "geniuses" at the Apple Store are instructed to fix the problem _if they believe_ it's Apple's fault, even if they are quite sure the customer cannot prove it.