Yes, we understand.
Graham is right. Look at his link.

What you do not understand is that the information in your interior (not linked) headers and footers is contained in section breaks within your documents. When you copy your document content into the new document, you are taking those headers/footers into the new document. There is no automatic process to deal with that.

If you want you can use the Word Toolkit for Advanced Management of Word Headers and Footers to see what is going on. That toolkit, though, will not "fix" the problem.

In trying to change things, Word cannot read your mind and figure out what needs to change and what needs to stay the same, you have to figure out a way to tell Word what you want.