Only because the private debts were nationalized in the last bailout round, which was basically a joint bailout of Greece's public finances and German/French banks, all of which were on the brink of insolvency. The bonds were previously mostly held by French and German banks, and the agreement did two things: 1) Greece was given a big chunk of money on the condition that most of it be sent back north to pay off a portion of their bonds; and 2) much of the remaining bad debt was shifted to public books, in the process being restructured with more generous terms. Greece has a large part of the fault in this whole saga, but they are not the only reason these originally privately held debts have now ended up on public books.
I do think from a realpolitik perspective Greece is playing hardball at the wrong time: they had a much stronger negotiating position in 2010 than they do now, when much of the "contagion" problem has been contained. But the government at the time stupidly agreed to a set of terms that solved the German/French problem while containing but not solving the Greek problem. Few serious economists at the time believed the package was a workable one for Greece, unless you thought some extremely optimistic projects of Greek GDP growth were realistic; it was seen as at best kicking the can down the road. But by 2015 when Greeks realized that and voted in a government willing to play hardball, they are no longer in a good negotiating position.