Or he did seek/receive permission, but no official communication has been released (oddly).
As a Belgian constitutional power, the king's consent to marriages of princes(ses) must be countersigned by a minister and published in the Belgisch Staatsblad/Moniteur Belge to be legal.
The Staatsblad may be searched online at
Moniteur Belge - Belgisch Staatsblad (July 1997-present)
There are royal decrees authorizing Prince Philippe and Prince Laurent's marriages and granting their wives titles, but none authorizing Prince Amedeo's marriage or granting his wife a title.