I can only speak my personal opinion about this because many people feel differently about this.
In my relationship with my husband, and even before we were married too, he knows my access information and sees where I go in the computer because I am always in an open room when I'm on the computer, however, he knows this information because I gave it to him, not because he ever asked for it.
I've never asked for his access information because I trust him, but again, he gave me the information.
People are entitled to certain privacies, even in a relationship, but there has to be a mutual trust there in order for this to work. If your lover is acting suspiciously and you feel they are hiding something, then maybe you should sit them down and talk with them about it. Not in an accusing manner, but in an honest and concerned way.
If you really think something is going on, you can always check the history filed on your computer and see what web sites have been visited for the past month, or however long your computer is set to hold the history.
Some people have nothing to hide, but don't want anyone else to have their access information because of the principle of it. They feel that if you trust them totally, then you shouldn't need that information. Some keep that information private because of fear that if the relationship heads south, then you have all their private information to do whatever you chose with it.
It can be a really sticky topic if you ask me.
Lezlee