Nonsense. If you work in a particular role with others at a company, you are able to measure yourself against them and others - not just output, but in lots of different ways. If someone is doing a particularly sloppy job or "fucking up constantly" it's your responsibility as a professional and as a decent human being to raise them up. You can do this by taking them aside and critiquing their work.
In my experience, criticizing the person just drags down their morale and usually doesn't motivate them, whereas criticizing their work sometimes motivates them to improve their work (it can also sometimes drag down morale as well, depending on how you go about it).
In especially toxic cultures, you need to be careful. It's unfortunate but true if you ever find yourself in one. Get out, get out fast if you are.
I think a key issue is that coworkers can be awesome workers, but HORRIBLE at critique. It's a skill that people aren't always good at. I know I could be better. A good manager will be great at this, and it's often best to let the best person at this do the talking. Managers can also be great as go betweens, and councillors for both sides, so that hatchets don't get buried directly into coworker skulls.
That said, the best teams manage themselves.
If you are a manager, while it is your job to occasionally criticize performance, it is never your job to criticize people. Further, if someone is "fucking up constantly," it's your fault. Do they understand the requirements? Do they have the training to handle those requirements? Is that the right role for them? Your job as manager is to make sure that everyone feels comfortable in their role and is able to further grow in that role or into other roles. If they're not doing that, it's your mistake.
In all cases, Wozniak is right. The only person you can criticize is yourself.