To partially answer my own question, from another page on the LOB website I found "the person concerned must have compulsory state insurance for retirement, disability and survivors' benefits in the new country"

So this seems a strange mix of Pillar 2 (BVG) assets being blocked by being subject to mandatory Pillar 1 (equiv. AVH/IV). Under what circumstances you would not be required to be insured for Pillar 1 I don't know.