The transparent background option works perfectly. Picture to People site generates thousands and thousands of logos per day with transparent background.
If you really have checked the "Get as a transparent PNG file" option, the background color you have seen when opening the logo file is the background color shown by the program used to open such file. Since the logo has a transparent background, in the Picture to People result page, for example, the logo is shown having as background the color of the page.
Besides, also it is important to know that not all graphic programs know how to correctly deal with semi-transparent PNG files.