I got these quotes from the Pali Canon - the scriptures used by Theravadans of Southeast Asia - from Douglas Duckworth, an excellent translator that has been up at TMC in Frederick several times in the last few days.
These words of the Buddha do seem to more than imply the presence of Buddha-nature - Thagatagharba - the underlying nature of enlightenment in all living beings. That is generally seen as the core teaching of the "Third Turning of the Wheel of Dharma", which is most often associated with Vajrayana (since it is required in order to explain how Vajrayana 'works').