Otherwise, nothing can be established at all, because for any statement there always will be someone's understanding of "internal monologue" for which the statement is true, and someone's else understanding for which the statement is false...
In practice, when you see people arguing about whether they have an "inner monologue" or can "mentally picture objects" on social media, it's more of a contest of who is the most unique in the world rather than anything that sheds clarity on our subjective experience.
Why does this matter? Stop being so pedantic. We're talking about a progression of ideas. Talking in your head is one form of ideas, but people can easily solve problems by imagining them.
We need to be at least somewhat pedantic, otherwise it's impossible to know what we are even talking about, and no way to establish anything.