That would be if the company were in Germany. But not outside Germany, there the freelancer is classified as "exporter" (both for US and EU clients).

the only issue is that you might be liable to pay social insurance (DRV), but only if they can show that you have only one long-term client, and I’m not sure if it applies to foreign clients, especially outside the EU (but it might)

AFAIK it doesn't apply to outside-Germany clients. The freelancer is viewed as exporter and contributes to German export economy. Mind you, a freelancer has no social safety net, no pension, exorbitantly expensive health care (900+ EUR) and no unemployment benefits either.

I think that’s why the DRV might step in and force a freelancer to pay into the social security system if they have a single client. If I recall it also applies to foreign clients, but I’m not 100% sure how far it extends. It’s definitely easier to bypass the DRV if your client is not German, but not entirely waterproof as I recall.