Do you live in Greece? Do you control the company from Greece? Do the company's activities take place in Greece? If so, the company is tax resident in Greece. Just ask any Greek lawyer or tax adviser.
Why do you think anyone would pay any tax anywhere in the world ever if this were possible? It's 2021, not 1991.
Furthermore, is it clear how an LLC treated under Greek law? Is it considered a partnership or a stock︀ company? If it's a partnership, you still have to pay personal income tax. If it's︁ a stock company, you have to pay Greek corporate income tax and any taxes due︂ on dividends or salary paid to yourself.
He's absolutely right, but also a little misleading. There is no tax︇ , in the US. That doesn't change your legal obligations at home in Greece.
Regarding exchange of information, you might want to read about FATCA, CRS, and tax residence in︈ general before you commit tax fraud. Or don't, and see what happens in a couple︉ of years.