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How important is a project methodology for the success of a project? How important are the 'social skills' of the Project Manager for the success of a project?

The modern Project Manager must have in particular in the current arena (just think of working with "virtual" teams in the context of globalization) a good dose of 'social skills' which may be more important than being able to apply a Project Management methodology. The latter is relatively simple and easy to learn. This does not apply to 'social skills'.
Are companies that insist that their Project Manager master a certain methodology as one of the 'knock-out' criteria for selection aware of this?