You can perform triangulation as far back as you want. It just makes it impossible to determine who is the common ancestor and how exactly the DNA was inherited (meaning along which exact path).
I'd like to bring your attention to Itsik Pe'er (who helped 23andMe on their algorithms) and his wonderful presentation about Identity by descent in medical and population genomics.
You can see in his work "The Genome of Netherlands" that he has identified IBD segments down to 1 centiMorgan which go back to an estimated 2200 BCE (unfortunately I still can't post pictures here on WT).
Please have a look. IMO it's not discouraging people to educate them right about science and a statement like you wrote is still just wrong (and note that my quote doesn't contain any "generally") and will be then copied over and over again. That's not helpful for the community or for spreading scientific knowledge about genetic genealogy.
I know you had no intention to spread false statements but like I pointed out in the peer-reviewed work linked in my answer autosomal DNA is accurate way beyond (!) 4 generations. Oh and 4th cousins isn't equal to 4 generations, that can be easily misinterpreted as well. Fourth cousins share a 3rd-great grandparent (5 generations), see.
Also, you're mixing things up in your recent answer. Triangulation is accurate, if you do follow all the rules set in place then IBD segments even of very small size (again, reference to Itsik Pe'er work) are validating the ancestral DNA was inherited from a common ancestor (albeit far back). So this has nothing to do with more false matches for smaller segments. All these statistics done are focusing on a threshold where the common ancestor is. So when it's written "false match" or more clearly IBS (identical by segment) it means that the common ancestor is outside (!) the genealogical timeframe that all DNA testing companies are trying to aim for.
Or why do you think do we have Neanderthal and Denisovan DNA in us? As per what most people misunderstand, those would be false matches, right? As the amount of shared DNA is too small. Yet, that DNA was inherited over the last couple hundred thousands years and more.
"Wrong matches" is something that happens when people don't know how to do triangulation and use tools like GEDmatch where you can easily trip by entering the wrong parameters.
As for Associate Professor Itsik Pe'er from the Columbia University you can find his impressive research brief here