Millions of people shoot unmodified Remingtons with no problems.
Just because they haven't had a problem YET, doesn't mean there isn't a problem. On the 1946-2006 rifles the problem is a flawed design. The 2007-2014 rifles were a solid design, but with a manufacturing defect.
On the older rifles around 1% of those manufactured have discharged with no trigger pull. 1% doesn't seem like much, but with 6 or 7 million manufactured that is a lot of guns firing. The vast majority have done no damage or caused no injuries. But there have been about 2 dozen people killed or injured.
The problem is that 100% of them could do it at any time. Just because someone has a 20 year old rifle that has never done it is no indication that it won't the next time it is loaded. Remington used a unique, quite complex, trigger design on those guns that no one else has ever tried. If internal parts inside the trigger (the trigger connector) align in just the right way it will fire without pulling the trigger. The engineer who designed the trigger discovered the flaw in 1946 and made management aware of the problem. He went as far as designing a replacement without the trigger connector, but Remington management ignored his warnings.
My rifle was manufactured in 1974 and I bought it in 1975. I first became aware of the issue in the late 1970's or early 1980's and scoffed at the idea. Until sometime in the 1990's when my rifle dropped the firing pin one day without me pulling the trigger. Fortunately it was unloaded at the time. I was able to get it to repeat it 2-3 times and it stopped.
I used the gun for another 20 years with no more issues, until 2 years ago when it did it again. Once again unloaded. After that I bought a Timney. That is only 2 incidents in over 40 years. Not a lot, but it did happen. I can understand why many people don't take this seriously. Just because you haven't seen it happen doesn't mean it doesn't.
The odds are that for most people you will never have a problem, that is certainly true. But I have no intentions of walking around with a loaded rifle knowing the trigger is a flawed design that could fail.