There is no proof of that. Even if you experience speaking and thinking as separate sensations, it may still be that they are actually "implemented" by the same structures in the brain.
There is in fact a theory that language is a tool for thought first, and for communication only secondarily.
One may not think in a common language used to communicate (e.g. English) but the way one thinks could be considered a language regardless, only specific to one's own mind.
Take for instance Google's translation AI. It developed its own intermediary language[1] which facilitated translation between languages and enabled it to even translate languages it had not specifically been trained on.[2]
[1]e.g. It had a "word" for dog that wasn't part of any existing language.
[2]e.g. it could translate Spanish -> French even though it was only trained on Spanish -> English and English -> French
This is a very sneaky argument that misses the point I think, you are effectively defining any sharing of information as a language, then using that definition.
