It's more than that. It can be shown that information could not travel between 2 points provably, so it's not like we're missing some communication method. We can show there is no intermediate communication method.

See the MIT introduction lecture on Quantum Physics:

https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...

I believe the experiment where this is shown is lecture 1, possibly 2. It's been awhile since I watched this but a great source of information.