The current account deficits in most peripheral countries were in fact led by very large capital inflows coming from core countries with capital account surpluses. The exposures of banks from core to peripheral countries more than quintupled between 1999 and 2008.
Competitiveness losses in the periphery were simply the mechanism that connected the capital account surplus and the current account deficit – that is, an appreciation of the real exchange rate caused by economic over-heating.