It's just silly isn't it. Of course they should be able to hand out invitations. Sometimes you'll get one, sometimes you won't. That's life. It's a good life lesson to learn - and part of a parent's job to teach it. If these situations are never allowed to arise, how do children learn about life?
I sometimes despair of modern society! Children aren't allowed to be left out, to compete in sports day (only in SATS results), and they grow up completely spoilt!
Seriously, isn't the correct thing to do in this situation to say to your child who hasn't been invited something like 'never mind, they can't invite everyone, another day it will be your turn to be invited.' And if they're really upset then say something like 'well, you must make sure that you remember it's sad to be left out, and make sure you are careful not to leave people out of games etc'.
If a child never experiences negative emotions, how will they ever develop empathy? And who wants their child to go to a birthday party, not because the child wants them to go, but because some rule says they mustn't be left out?