I think people are just using the word "think" differently. They may have picked up a different meaning for that verb than you. For them, thinking == inner vocalization. It's just a different definition. They would not call imagining things or daydreaming or musing or planning action steps as "thinking".

Also, many people simply repeat facts they were told. "We need words to think" is simply a phrase this person learned, a fact to recite in school settings. It doesn't mean they deeply reflected on this statement or compared it with their experience.