I have the same issue in v 2.8.6 - I tried with both png and jpg (again, checking for any borders, dropshadows), and like the original questioner, my logo has a white background. Both produce the shaky white outline.
I've got around it by using GIMP to change white to alpha, but I'd be interested to know if anyone else has a workaround, particularly as the original questioner mentioned transparent backgrounds were still producing the white outline.