If I set up a US llc as a Belgian while residing in Belgium, Belgian tax authorities will claim the center of control is in Belgium and claim it is a Belgian company.
Of course not. They'll just claim your llc needs to pay local corporate income taxe, VAT, pay local social security, dividend withholding tax, ... on top of whatever needs to happen to keep US authorities happy.
Sounds like bad advice. Registering a local company in the Netherlands is super simple, tax is an online portal, everyone could do it. Setting op a foreign Delaware company means you're then dealing with international tax issues.
Unless you also personally relocate, then it probably makes sense.