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Harrow said..
I've heard all the stories, but this is the first time it's happened to us.
My wife went to the physiotherapist to fix some hip pain she's been having. That night she discussed with me the physio's idea of trying orthotics to address the issue by preventing overpronation of her foot. She has sent no text messages or emails about the subject and has not done any internet searches related to the issue. Next day she is receiving ads on her phone about shoes that offer arch support.
Creepy!
Yeah, that explains all the ads I am seeing too... must be one of the neighbours that is googling stuff

I suspect that anything that goes through Gmail or any other online email service is filtered for keywords.
Then again, if a phone can wait for 'hey siri' or 'ok google', is it doing anything else with words it hears?
Maybe you can try an experiment. Start uttering different words in different places, send emails with different content, and see which ones get a result?