...not my experience either. Not with laptops, cameras, phones, etc. The biggest concern to me isn't safety - it's the gamble of if you got a bad/good/better battery with the knock-offs (to me a counterfeit is a third party that is labeled to look/scam like a genuine OEM). Occasionally, you may get a knock-off that does better and last longer. After all, the cells probably came from a decent place. However, it's the QC and guarantee that makes the difference.
Manufacturers (OEM) have a decent amount of reputation to uphold by being sure that anything they send out meets a certain expectation (if your original laptop battery lasted 4 hours and your OEM replacement lasted 3, you won't be happy). So, they batch test and try to get a consistent group of materials and components. If you have a problem with your new one, they will usually accomodate and take care of the issue quickly.
Third-party batteries are a gamble, as they may have sourced parts from the same supplier as the OEM, or they may have bought the rejects from some QC firm (happened to many capacitors!). It may work great for the first few months you have it and it may just quit one day. Or, it may last forever. If it quits, is the maker going to be around, care, or cover you to get it replaced?
I prefer to lower the odds a bit and at least if my OEM quits in the middle of an important time, I have a company I can b*tch at. Some may say, yeah, but you can get 3 cheap ones to carry instead of the 1 OEM. But, space in my pockets/bags are a premium. I'd rather not have to dedicate a whole compartment for "backup" batteries. That, and not look stupid when my camera doesn't fire, laptop doesn't power up, or phone dies in the middle of a call.