I think that if you keep things straightforward and simple, then you can avoid getting fired due to someone's else's mistake. If you tend to allow people to take advantage, then they will certainly put a lots of blame on you and this is how others can get away with things.
The mistake of another person is something that you cannot be able to prevent or influence in your working place. The only thing that you need to be worried about is if the management is going to be punishing every of the employee as a result of what one person did. In a situation where by a company do this kind of thing, I don't think I'm going to be comfortable working in such establishment.