It certainly begs the question, should someone just trust Amazon’s assurances? Given that “privacy” in the US is a much more slippery term than in Europe where there are actual legal definitions, and given how much Amazon can tap into whatever is going on in an Alexa, I would say no, one should not trust them.
I’m reminded of a friend who has an Alexa. She developed a cough last winter and not long after started getting Amazon ads for cough remedies, even though she did not look for any related products online or in email. But her Alexa was on and heard the cough…