Yes, Nature is absolutely going to reject that paper. I went to grad school at one of the very best programs in the world and know a ton of people who attended

Yes, Nature is absolutely going to reject that paper. I went to grad school at one of the very best programs in the world and know a ton of people who attended programs of similar caliber and had world renowned faculty as authors on their papers. People got their shit rejected all the time. Yes, the bias you describe that makes people respect papers from well known sources more than papers from outsiders is real. But it isn't nearly as extreme as you describe it.