I had never tried I2C in the Arduino environment on Edison (only in node.js/linux) so I thought I would give it a try. I tested an I2C 16x2 Character display and everything worked as expected (no special commands/etc to get I2C working).
I am using a shield that connects to the I2C bus through A4/A5 (according to the schematic the SDA/SCL lines are connected to A4/A5 as well). You could try using A4/A5 instead, but I doubt you will see different results. Are you sure you don't have SDA/SCL swapped?