I entirely agree with you, and that’s the point I was making at nosqleast when I said “that’s what makes it a theorem.” True things are simply true, and you don’t choose whether or not to have them affect you.
A video of that talk is at https://nosqleast.com/2009/#speaker/sheehy and you can jump 16 minutes in if you don’t want to watch the whole thing.
The CAP theorem doesn’t exist in a vacuum. It came about due to real, inspiring work on serious problems. Eric proposed it due to the changing needs of applications on the internet that needed to make their own business decisions about availability in the face of inevitable host and network failures. The one-size-fits-all model that much of the RDBMS world followed in that regard was just beginning to crumble, and he saw this earlier than most.
I would argue that Riak correctly claims a deeper level of influence here, because it is not just obeying that theorem (as everything does) but is a system based on the idea of explicitly helping the application layer (not just the database layer) be able to make the right tradeoffs.
To carry your analogy forward: everyone is obliged to obey the laws of physics, but some people are also influenced in an additional way by the words and ideas — not just the results — of Newton, Einstein, Feynman, and others.
Others make CAP choices because they must. “Influence” here can mean building a system while being explicitly conscious of the reasons why you must make those choices. Having that influence is not unique to Riak, but it does remain a meaningful distinction.