This summary is not the rule. The rule text controls.
If someone gets added to a lawsuit who shouldn't be there, or if someone who should be part of the case gets left out, that mistake alone won't get the case thrown out. Courts understand these mix-ups happen, so the rule gives judges an easy way to fix them.
A judge can add a person to the case or remove someone from it at any point while the case is going on. This can happen because one of the sides asks for it, or because the judge notices the problem and decides to fix it without anyone asking. The judge just has to make sure it's done fairly for everyone involved.
The judge also has the power to split up claims. If a case involves several claims against different people, the judge can separate one of those claims out so it moves forward as its own thing. This can help keep cases organized when too many people or issues get mixed together.