I'm assuming you don't normally expect strict secrecy from your wife regarding your correspondence, your house, your phone, and your...privates. If you do expect that, you'll probably have to engage in non-default behavior. Just like here.
That house, phone, and privates all belong to her because I married her. Using your analogy, would it be too much to ask for a purely platonic web browser without everyone flaming me as commitment phobic?