I hear this sentiment from Europeans often, and I’m sure it’s true. But obviously the languages you’re talking about have a lot more in common with each other than they do with say, Chinese or any other “eastern” language.
Well, yes, it obviously won't work for any random pair of languages. E.g. even in the European languages, you have "famous" exceptions like the very isolated Finno-Ugric language group (in Europe represented by Finnish, Sami, Estonian and Hungarian) that have pretty much nothing in common with the rest.