Because there's probably something similar to a "Today's Date" field in the document somewhere which will change simply from the act of opening and closing a document.
Sure there must be a technical explanation, yours is very plausible but it doesn't change the fact that this annoyance only happens in MS Word (that I know of); it doesn't happen in MS Excel or OpenOffice Writer for example. If there's a 'today's date' then they can just add an 'last updated date' or similar and keep track of the file changes.
It's more aggravating if we take into account how popular, old and big the application is.
