OK, I found the answer after some searching on the Apple boards. In case someone else runs into the problem, here is how to fix it:
For some bizarre reason, when you click on the text in the copied box, it selects the whole box instead of adding the cursor where you clicked. So you have to first double click on a word (which selects the word) and then single click again to get a cursor.
Go figure...
Note that in the original box, this is not an issue as you can get a cursor simply by clicking inside the text the way you normally would.
Bo