Is the Prophet's (PBUH) saying to Aisha, "I am fasting," considered evidence for verbalizing the intention?

The Hadith to which the questioner referred is authentic. The Prophet's (peace and blessings be upon him) statement, "Indeed, I am fasting," is an informative declaration, not an utterance of intention. It is not known that the Prophet (peace and blessings be upon him) ever uttered his intention before acts of worship. This is what Sheikh al-Islam Ibn Taymiyyah explicitly stated: that uttering the intention is neither obligatory nor recommended.

His (peace and blessings be upon him) saying during Hajj, "Labbayk Allahumma Hajja (Here I am, O Allah, for Hajj)," is not an utterance of intention; rather, it is a form of talbiyah (invocation) for what one has entered into ihram for. It is a form of remembrance (dhikr), not an announcement of what is in the heart. The criterion for intention is what is intended, not what is uttered.