Manning levels is a huge issue in merchant marine fleets around the world, exactly for the reasons you suggest: the bottom line vs. safety. Minimal crewing levels lead to overwork, fatigue, lack of concentration, human error and, inevitably, accidents. Here's an article by a former merchant marine engineering officer. His experience is in the British merchant navy but it applies to any other merchant fleet: http://www.brighthub.com/engineering/marine/articles/106516.aspx. One could likely find plenty of similar articles with a search.
News reports indicate RENA had a crew of about 25. RENA was built in 1990 whereas EMMA MAERSK was built in 2006, and benefits from technology not available at the time of RENA's construction. But that still begs the question: was a crew of 25 appropriate for RENA, given its age and technology? Is 13 an adequate crew for EMMA MAERSK, given its technology? I don't know the answer, except there must be some absolute minimum number that is necessary to safely operate and maintain a large, modern merchant vessel. And a crew of 13 must be at or very near (or even below) that minimum.
Here's a striking photograph of RENA in her current situation: http://gcaptain.com/rena-update-substantial-structural?32463.
Ron Carlson, Webmaster