It could be solved, but is it really ?
Shall I remind you of this: https://en.wikipedia.org/wiki/2013_horse_meat_scandal#UK_Inv...
The blockchain doesn't offer a technological solution that couldn't be done with a centralized authority (I particularly like the way passports rfid reading involves certificates signed by each country). But it offers means to achieve that even if nobody safe enough wants to host the bloody service.