I think the point he's making is that it isn't as though the European Parliament is "standing up against" the EU or whatever: the parliament is part of the EU;

I think the point he's making is that it isn't as though the European Parliament is "standing up against" the EU or whatever: the parliament is part of the EU; you could rewrite the headline as "EU rejects EU plan". That view may not fully capture the subtlety of the matter though.