True, though native speakers do distiguish a good swath of "homophones" by differing pitch accent---e.g. in the standard dialect あめ means "rain" if the pitch drops on め or "candy" if it stays level. To a native speaker, these sound as different as the two ways of saying "present".

If you grab a native Japanaese dictionary that has accent indicators, like 新明解国語辞典, there really are surprisingly few true homophones in a typical vocabulary.