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I think if someone already has the thread open (so that message box is still visible) then they can still post. I'm guessing anyone that clicked on the thread after the 1000th post was posted wouldn't have been able to post one (an awful lots "posts" there sorry )
I think that when loads of people are repeatedly posting to get rid of a thread, lots of posts get through at exactly the same time, so the number of posts exceeds 1,000.