Found a fix to this problem in another thread and thought it might be helpful to post it here:
To fix this mess that Squarespace has created with their asinine default settings, do the following:
Menu > Design > Section Themes
Select the theme of the section where your images are displaying incorrectly. You'll have to do this for all offending sections.
Click on the offending image, which selects it's widget type in the styles options list. Choose 'image overlay' and move the white circle in the bottom ribbon all the way to the left. This will then display transparency correctly.