why would you bring another child to a party they're not invited to.
As many have already explained, if it's an open venu, you aren't bringing them to a party technically and they're just there to play (separately from the party); you wouldn't expect them to be included in food, or games or party bags etc.
I suppose the real answer to your question is that it's simply more convenient, for all of the reasons pointed out above. And since parents' evenings and weekends are busy enough, I would refuse to deny them of making life that bit simpler and less chaotic by bringing another child along, if it helps for WHATEVER the reason, especially when there's going to be plenty of other children you don't know. I will say it again, but I do think it's shameful that you tried to do this to the other mum.
Would it be fair to think it's actually impossible to have a party if someone is going to bring random siblings anyway?
This is absolutely possible. Book somewhere exclusivly that has maximum number of children allowed and when you send out invites say,
'Unfortunaly, due to limited capacity at the venue, we will be unable to accommodate siblings."
I have a local pretend play town that has a maximum entry and is one of the few parties I've been to where siblings weren't accommodated, due to space.
However, I think it'll pay in the long run if you tried to be more welcoming and less judgemental (in general, probably) to these parents, OP. There will be plenty more parties down the line and they'll be with the same group of adults so it really doesn't make sense to give yourself the label of 'controlling OTT mum' so early on.