I don't really buy any explanation here. The reason why thinking out loud with someone beats thinking alone is because when I'm alone I'll loop a lot more.

My reactions to thoughts that I myself have had are stereotyped and repetitive (every reaction is typical of me.) Reactions to me that come from another person are going to be different than those, and in turn stimulate me differently. Thinking tends to be an enumeration (then elimination) of possibilities, and that random input helps with the enumeration part by keeping me out of local minima.