This kind of makes sense. If a boarding pass has SSSS on it, TSA is supposed to make a notation on it that you have been screened.
So, it stands to reason that if the WC issues you a new boarding pass on it, which still contains the SSSS, then you will be presenting an SSSS boarding pass at the gate without the TSA notation that you have been screened.
I'm not quite sure what the WC can do in this situation. Don't know if they can issue you a BP without the SSSS, they probably can't override. And, if they give you a new BP with the SSSS, there probably is no notation that they can make that would be allowed (they are not TSA.)
Now, in a logical world, they should issue you a new BP with the SSSS, and you should be able to retain your old BPs with the TSA notation showing you were screened, and this should be accepted at the gate as proff of screening. However, given that we are talking TSA here which is part of the Bizarro world and not the logical world, this might not work.