Well, if it is not a bug, it is one serious design flaw... Here is what I finally came up with (and it sucks):
Create a new "Search Results Page" in your SearchCenter. (My example: SearchforClasses.aspx)
When you create the page, modify the "Search Core Results" web part. Under the "Miscellaneous" section, you have to specify the scope you want to use. of course, there is no way to BROWSE to it, so you have to remember what you called it. Click OK.
On the "Results" page, add a new TAB and call it something (My example: "Search for Classes"), then type the results page name you just created before this step (Ex: SearchforClasses.aspx).
Publish the page (don't use "check-in for draft" because that seems to send the page into electronic la-la land).
Now, here is the really stupid part. The users have to do an "All sites" search and get the results. THEN, the can click on the newly added tab and see the results they REALLY want. If they START at the new tab, the dumb thing jumps back to the "All Sites" search. Now, there may be a way to fix that behavior, but I haven't had time to mess with it since putting in this "very temporary" workaround (I dare not call this a "solution!").