It'll let you granularly authorize first party access what data you have in your pod, but there can’t be any technical guarantees with regards to illegitimate sharing or otherwise copying (many might at least cache, for instance) – nor about what is collected and shared outside this system. It's own documentation even states this, if you dig a little.
I keep seeing data-hubs and identity-providers touting themselves as solutions to the web's privacy issues, but I don't see how they actually solve anything. It seems like an attempted technical solution to a social problem to me.
The real problem with data how data is used these days is really that a bunch of data is collected opaquely, unethically, and in some cases illegally – and possibly shared. The whole system including data brokers and real time bidding is out of control.