Can someone who was appointed Power of Attorney in 2011, legally obtain bank statements for the person for whom they are POA for those years previous to their appointment? I.E. POA appointed in 2011, requesting past statements for years 2010, 2009, etc.

I would recommend reviewing the language in the POA for any clues as to what the principal would want (and don't rely too much on generalizations). There could be legitimate reasons for reviewing past history as it relates to a current situation. On the other hand, the attorney-in-fact might just be doing it for personal reasons. Did they explain why they needed the information? I don't believe that a POA is necessarily restricted time wise as a rep payee is for social security payments.