On a mass scale, maybe 0.2% of people would double check the source page. The rest would be unknowingly influenced to eat "healthier" by Google.
Yes, this seems unlikely. But so has much in the last 5 years.
Why are we deliberately charging head-first into social man-in-the-middle attacks? We already don't trust each other enough. LLMs lie, and lie often. Why should we trust them for anything?
Would you be OK asking a LLM what food is safe for an infant, or a pet dog? Without checking the source?