I was using gwt-dnd-2.6.0.
I changed it to version 2.6.4 and it started working as expected.
Seems to be a bug in version 2.6.0 of the gwt-dnd library, but I've
looked into the issues in the gwt-dnd site and didn't find any
references to it.
Anyway, my issue is solved.
Thank you for your reply