This behavior shouldn't be rewarded.
If something's not worth your energy, just walk away. Don't stew so hard that you need a webcomic to reassure you that you're a well adjusted person that's obviously in the right and your opponent is a grotesque sea creature that doesn't any social etiquette.
But there's something really cool you could do that would educate the person you're talking to (both in terms of instructing them how to google, and communicating to them the key thing you've found out) -- all the while being polite and formal! --
Say something like "I used this search query [foo bar] to discover [result-x&y]." Do that enough times and you'll make the whole world a better place. :)
That is why it's best to just give a domain name AND describe a suitably qualified query.
When I make a claim, I’m not writing a thesis or going for my PhD. I’m just reciting some blurry memory that such and such may be so. People that challenge me to provide peer reviewed citations of such claim are not engaging in civil conversation.
Saying "Google it!" tells me the person probably has no source, no idea how unreliable the information floating around on the web can be, and no understanding of how to find and appraise a good source.
Even on searching in Google Scholar, we sometimes find that the research literature often includes papers that offer divergent estimates and opinions.