One of the fascinating features of the data on credit default swaps is that they exist in very similar terms for both countries and companies. In this case, if (i) the recovery rates on public and private bonds are the same, and if (ii) the stochastic discount factor pricing assets is similarly (un)affected by a default on public and private bonds, then if the CDS premium paid on a company is smaller than that of the country this means that the market is believing that there is a higher probability that the country will default vis-a-vis the company.
But how can this be? After all, a country on the verge of defaulting can always simply enact a 100% capital tax on the company; whatever money could be channeled into paying the private debt could be diverted to pay the public debt beforehand. It must be that the country is not willing to do so, that is that it would rather go bankrupt first before letting its main companies go bust. This can make a lot of economic sense, especially if markets are harsher on companies rather than countries that defaulted in the past. But seeing the private CDS below the public CDS does reveal that the markets think that the country may not just be unable to service its debt; it is also considering choosing to do so with a high enough probability.
In Greece, there are already a few companies with a lower CDS premium than the government. This is not the case in Portugal or most of the other European countries going through a debt crisis. Portugal, Spain, Ireland, Italy and the UK may have public debt problems; but Greece is in a league of its own (at least for now).