Rihanna sings Te Amo with a strong Caribbean flavor. She's from Barbados after all.

Maybe, because that song matches that Caribbean flavor the choice was for me instead of my.

She has certainly done a lot of work to change her accent into the standard American.

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In Wikipedia we read "The use of me instead of my was also attributed to Irish English influence: for example, "That's me book you got there" for "That's my book you got there". An exception occurs when "my" is emphasised: for example, "That's my book you got there" (and nothis)." http://en.wikipedia.org/wiki/Scouse