Appliances with the full Kite/CE marking can still cause problems too, i.e. the marks are only from a sample that is tested, a bad batch or single poor solder joint can cause issues.
It's worse than that. All these quality frameworks have the concept of self-certification. If inadequate quality most likely wouldn't directly cause death or serious injury then it's not worth the time and expense to insist on oversight - so the manufacturer applies the mark on their own authority and the first time an independent assessor would check it is if there's a formal complaint. Until / unless that happens to them nothing stops makers or importers fixing the mark without doing any tests at all. Of course if they get caught they could get a fine or even do time, but that's not likely. EM shielding is definitely the sort of thing cut price manufacturers won't test properly even on a sample item.
Not every kind of CE mark can rely on self-certification, a CE marked pacemaker for example has to be tested by an independent third party, but "low risk" things like a beer fridge or a mobile phone charger are usually self certified and thus their quality is indeterminate. You are of course entitled to a full refund if you buy something that's unfit or not as described - and a CE marked item that wouldn't actually pass qualifies as both - but in my experience on very cheap unbranded junk where the problems are most likely people throw it out when they notice a problem rather than trying to get a refund.