If your example had "Validate any details before sharing them with the user, with multiple sources" as the system prompt, it was using a model that is strong at following system prompts precisely and had access to some basic tools, then it'd spend maybe minutes more, but the answer would have been way more accurate.
But no, Google want "the new search results" (LLM hallucinations) to be on top, so we end up with "sounds plausible" answers instead "Collection of evidence from reliable/semi-reliable" or similar, which sucks. We could have quality, but it's too expensive/slow, so we get slop instead, just to maximize for speed and convenience.