If you tell someone that the problem lies in the way he speaks and your very different styles of speaking, and this person says that he can't help it that he doesn't speak like a grandma, surely he means, "We have very different styles of speaking because I don't talk like a grandma", and therefore mean that you talk like a grandma- - No, it needn't mean that. Only more context would make that clear. In fact, Jerry's last line above seems to contradict your assumption: Jerry is only describing his own way of speaking.
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