Sometimes using fewer words enhances clarity. Country A has debts of 100 Euro. The debt gets restructured by 50% so that Country A now only has debts of 50 Euros. How has this transaction magically pushed losses onto public books of Country A?
(I wrote "part of" because there was a haircut involved for the private lenders. They /did/ take a loss.)
Edit: tpyo.
Now there is a crisis, and the unsustainability of the public debt of country A is undeniable to everyone, so no-one will buy the bonds, well maybe for 5 EUR. However, through lobbying etc. a deal is struck so that Country B lends Country A 60 EUR to buy the bonds for the artificially high price of 53 EUR, thereby allowing the banks to escape the full writedown from 100 EUR to 5 EUR, but pushing 48 EUR of unrealized bankers loss onto the public books of Country A (debtor) and Country B (creditor).
Nevermind the theoretical principles involved, the actual numbers are quite different from what you probably believe: All in all, around 200 Billion Euros of private creditor debt was restructured:
1) 107 Billion Euros were simply written off
2) 62,4 Billion Euros of old private bonds were exchanged into new private bonds
3) Only 29,7 Billion Euros were paid out to private creditors and shifted onto the books of other Eurozone governments.
I don't see we disagree about the numbers? Of the 200 Billion, only about half of the losses were realized. The rest was pushed onto public books (as new bonds or as bailout-loans).