The word you're looking for is "meme", as in a commonly repeated opinion that propagates through a population.
It's never been particularly accurate. Anything as large as the modern democrat party is going to have all sorts of opinions, which is one thing a lot of, uh, twitter style opinions, tend to miss. Ocassio-cortez and Manchin were both technically part of the democrat party at the same time, for example.
I've also read this sentiment online quite a few times, but find it rather unconvincing, especially if world politics encompasses more than Europe, the Anglos and Japan.
Left/Right is a pretty rough categorization to begin with, and things we associate with it in a liberal democracy might not hold globally. In China, the left wing of the CCP and other parties is generally regressive, wanting to go back to policies more in line with Mao, while the right-wing is economically more akin to our european liberals, but also socially progressive for things like lbtq rights. In South America, the left wing is usually economically statist and redistributive, but might be rather conservative on some social issues. There's also the whole liberation christianity movement. Japan as a country is way more conservative than the US.
Going back to a US-EU comparison: I think it is fair to describe the Democrats as centre-right on economic policy, especially when it comes to taxation. Outside of the UK, almost all countries in the EU have less qualms about high taxation levels, and it is obvious that a lot of senior democrats are in the pockets of rich donors and Wall Street.
On social issues I feel like it is different though: Open borders and immigration in general is significantly more controversial on the left side here in Europe. Things like being against against voter id is considered cooky by basically everyone. And the US is often leading the way on issues, as can be seen with gay marriage and cannabis legalization.
A simplistic left/right analysis does not do justice to the complexities of voter ideology and policy. In fact, I think the more this kind of analysis makes sense, the less mature the democracy tends to be, as it indicates that people look at it as a teamsport.
