If my machine and your machine can find each other peer to peer, then as long as we have each other's IPs, we can find each other's websites (without domains). 

If you say "I run Google.com" to a resolver service, and I ask that resolver service to route me to google.com, I'll get you (and whatver site you serve me). 
If I ask a DIFFERENT resolver service for the same domain, I might get a different website. 
Non-global. 

But this is fine and good. Maybe I actively want YOU to be my Google in the some particular context, so I use that resolver in that context... And when I want a different provider to be "my google" for a different context, I point to that one. 

Silicon valley can provide its own resolver and everyone can call that "default/global" if they want. But the global nature of it is just window dressing. There is no global, beev