Got it!
Yes, finally got it!
a) there was nothing wrong per se with the NVIDIA driver
b) there was, in my opinion, a lot wrong with the user interface of the 'profiles' section of the control panel :)
The thing is that when saving a profile, you get to choose things that the profile will include. Basically these are devided between 'driver' options and 'desktop' options. There was some box in the 'desktop' area that resulted in the behaviour I described when checked. The description of the box TOTALLY did not relate to desktop icons so I didn't get it even though I went over it many times.
Finally, using trial and error I found the right box to UNcheck! I won't go over it now since probably this is not interesting to anyone that has not come across the problem - if you want to know, I'll post screenshots.
P.S. thanks Viper for the comment. When one is locked up in a problem any input helps!