I've never liked that witticism. For one thing it breaks down really quickly - ie by that logic Welsh is a dialect of English, and Walloon French is a dialect of Flemish. It's also fairly irrelevant to me what a government thinks is a dialect when I want to discuss languages. IE ethnic chinese can call languages that are mutually unintelligable 'dialects' all they want, it doesn't change reality.
The Yiddish original, "a shprakh iz a dialekt mit an armey un flot", was targeted at people who refused to view Yiddish as an independent language, but rather just as a dialect of German. The point was that if Yiddish-speakers had their own country, those people wouldn't have said that.
Similarly, I've heard several non-Bavarian Germans claiming Bavarian isn't a language, while the Bavarians claim it is.
People use it like it's a rule, but it was more a specific quip about Yiddish, and how many saw it as a dialect of German, rather than a distinct language.