I'm not a cryptographer, but the way I'm seeing it is that the reconversion takes place at the convenience of the receiver, not necessarily as a single transaction. If it happened as a single transaction that would provide plausible deniability (not good enough in countries that use beheadings) but not zero-knowledge.
So let's wait for a real cryptographer to tell us which it is.
I think you are right. If you look on slide 7 here:
https://docs.google.com/presentation/d/1yX2jN618Rnzs4g2ri_utdKdHbny6-xnRcPhOuhLNGB0/edit?pli=1#slide=id.g577a31a2a_3351You will see that once Bob got the SDT, he could then send the SDT to carol without ever transferring the SDT back to SDC. If true it would mean it would be much more private because you don't have to transfer the SDT back to SDC right away, you can send it around as well. Seems pretty genius, but hopefully others can tell us better if this is truly how it works, because honestly I am still wrapping my head around it. Afraid to try it out yet.