Sounds like somehow Word's Options got set to make that a read-only
file.  This read only has nothing to do with Properties; it's how
windows will open the file; read only in this case.  It is settable on a
per file basis.

Do the opposite to remove the read-only.  Look in Word's Help for
read-only
and it should explain that and more.

Prompt to open a file as read-only
You can suggest, but not require, that users open a document as
read-only. If a user opens the document as read-only and changes it,
that person can save the document only by giving it a different file
name.

 1.. On the Tools menu, click Options.
 2.. Click Security.
 3.. Select the Read-only recommended check box, and then click OK.
 4.. Click Save.

PS Or, maybe a template problem:  Just noticed:

Open a file as read-only
 1.. In your Office program, click File, and then click Open.
 2.. In the Look in list, click the drive, folder, or Internet location
that contains the file you want to open.
 3.. In the folder list, locate and open the folder that contains the
file.
 If you can't find the file, you can search for it.

 How?

 You can search the titles, contents, or properties of Microsoft Office
files, Microsoft Outlook items, and Web pages.

   1.. On the Standard toolbar, click Search .
   2.. Do one of the following:
   Search for a file or Outlook item containing specified text

   You can find a file or Outlook item containing text in its title,
contents, or properties.

     1.. In the Search text box, type the text to search for in Office
files, Web pages, and Outlook items
     Tips

       a.. Type a question mark (?) to match any single character in
your search text, or type an asterisk (*) to match any number of
characters.  For example, s?t finds "sat" and "set"; s*d finds "sad" and
"started."
       b.. When searching for Outlook items, use natural language
searches. Natural language searching is only supported in English
versions of Microsoft Office XP.
     2.. To limit where to search, in the Search in box, select one or
more drives, folders, Web sites, or Outlook mailboxes. To search
everywhere, select Everywhere.
     3.. To limit the types of search results, in the Results should be
box, select the types of items to find. To find all types of files, Web
pages, and Outlook items, select Anything.
     4.. Click Search.
   Search for a file or Outlook item based on one or more properties

     1.. In the Basic Search task pane, click Advanced Search.
     2.. Enter one or more search criteria.
     How?

       1.. In the Property box, choose a property from the list or type
in a property name. The Property box displays the properties available
in the currently open document.
       2.. In the Condition box, choose a condition from the list, or
type in a condition.
       3.. In the Value box, enter the value to associate with the
condition.
       4.. If previous search criteria exist, click And to add a
criterion that must be true in addition to previous criteria. Click Or
to add a criterion that is sufficient regardless of previous criteria.
       5.. Click Add to add the search criterion.
       Note   If the value is invalid for the condition or property,
the Add button is unavailable.

     3.. To limit where to search, in the Search in box, select one or
more drives, folders, Web sites, or Outlook mailboxes. To search
everywhere, select Everywhere.
     4.. To limit the types of search results, in the Results should be
box, select the types of files, Web pages, and Outlook items to find. To
find all types of files and items, select Anything.
     5.. Click Search.
 In the Search Results task pane, you can take one or more actions on
the search results.
 How?

   a.. To quickly view an item's properties, rest the mouse pointer
over the item.

   b.. To open an item in its default editor, click it.

   c.. To open an item in an Office application, click the command
button following the item, and then choose Edit with <application>.

   d.. To view a Web page in a browser, click the command button
following the item, and then choose Open in Browser.

   e.. To create a new document based on the selected item, click the
command button following the item, and then choose New from this file.

   f.. To copy a hyperlink to the selected item onto the Office
Clipboard, click the command button following the item, and then choose
Copy link to clipboard.

   g.. To view all properties of an item, click the command button
following the item, and then choose Properties.

 4.. Select the file you want to open a copy of. Click the arrow next
to the Open button, and then click Open as Read-Only.