moonshineshadow: Alright, hope they can figur out what is wrong fast :-)
I heard back from GOG Support, here's what they said:
[...]
If you have logged in not longer than an hour ago, and decide to change your account email address, or avatar, you will not be asked to input your current account password.
However, if an hour have passed since you've last logged in to GOG.com, password will be required to make any of those changes.
And after asking for some further clarification, just to make absolutely clear:
You can change your avatar and username without the need to enter your GOG.com account password for an hour after you log in to GOG.com.
Looks like my joke-post was spot on. :-)