
I certainly don't confuse 'web' and 'public' since I do have my own non-public information tucked away in a sub-domain of my own website.
It is very reasonable for a national library to take and store copies of any published document (I see it as part of their job). However, the key point here is the word 'publication'. (Notice the structure - PUBLICation). I don't consider web based storage of private and limited access data as 'publication'
I followed the link you gave and was horrified by what seems to be happening in Denmark. If this is the route that Germany is taking (apparently not but maybe 'not yet') then I'm sure that the UK will not be far behind, if they aren't already secretly in front.
If this is followed through then who will feel comfortable storing information on an internet connected web-server?