Well, it is solved. I thought run as administrator would be needed for the updates only. But everything is solved when I run as administrator. This is a bit weird. No other software has this problem for me. The update install did work this time, without manual download. The "corrupted" version works as administrator.
Stylepicker thought it needed updating every time I had a different user (user vs administrator). So, using BIAB as administrator only, seems to be the solution.
Thanks for replies.