This is just straight up not true. You need a legal body in a country if you want to hire someone on payroll there, you most definitely do not need one just to sell your goods and services, that's the entire point of the single market. It sounds like you've misunderstood a second hand recollection of someone else's struggles?
> You need a legal body in a country if you want to hire someone on payroll there
Even this is not strictly true. One can often just register a foreign company with the local tax agency for a direct hire. The most frequent scenario is that a foreign hire comes through their own legal entity, as a hired contractor. Now, the sad part of that statement is that often a hire comes as a hired contractor not because of cross-border taxation, but because of tax management reasons. In some EU countries, high value employees cost three euros in taxes for every two euros paid after taxes. A lot of people prefer to set up a corporation that allows them to better manage that majority of their income that goes to the tax office.
That's not employing someone in a different country though, that's contracting. And it's the same arrangement you can use to hire someone in the US from the EU.