Yes this is true (although also true that it doesn't mean people are at fault for failing to notice signs) and is a major branch of study in psychology.
It's more usually a case that procedures aren't being followed properly because people find them inconvenient, or don't understand the need for them, and there is no oversight by someone who does understand the significance of these things. It is very rarely malicious negligence, although sometimes it is found that someone who was responsible for safety guidance being followed has ignored or dismissed warnings given to them.
And sometimes the signs that something is close to failure can be spotted by an expert, but a layperson/people who interact with or see the item every day wouldn't recognise them necessarily. But it can be incredibly difficult to predict exactly which behaviours or warning signs will lead to disaster whereas which won't, because when you're talking about signs or missed safety protocols which go unnoticed for years, these are usually problems which will only cause disaster when triggered by something which won't happen the vast majority of the time (like you might never find out your seatbelt is defective as long as you don't have a crash, which is why they are checked at MOT).
With every major disaster there is usually some kind of investigation/inquest to see whether lessons can be learned from it. And most safety regulations are, as they say, written in blood.
The thing is that the way we understand risk as humans is calibrated much more to risks which are highly likely, like getting burned by sticking your hand into a fire, so safety precautions like a fireguard for young children make sense, but risks which are much less frequent, like a building fire, are difficult for people to process in the same way and so things like propping open a fire door or locking a fire exit just seem like ordinary/practical things to do day to day and it's only in the event of a disaster where these things are found to have contributed to deaths that they are looked at and people say how terrible, this should have been done differently, it was a disaster waiting to happen.
In general we take our cues to act from how people around us are acting e.g. there is a study where they wanted to know how people would respond to signs of fire by asking study participants to sit in a waiting room which was also half filled with actors. When the actors responded with panic to a smoke alarm, the participants evacuated the room. When the actors ignored the alarms, the participants also ignore them. Even when smoke was pumped under the door of the next room, the results are the same. So following what the majority seem to be doing is highly influential on people's behaviour, even if they have cause to believe their life might be at risk.
There is also the bystander effect, which is where people don't raise concerns because they assume that somebody else will have already done so.
There is a very good book discussing some of these themes called In The Heat of the Moment by Sabrina Cohen-Hatton.