Circulating Tumor Cell vs Circulating Tumor DNA
I'm not sure the relationship you are trying to build between EMT and cancer cells.

Yes some "healthy" cells undergoing EMT could (due to specific underlying mutations) result in cancer cells but such a phenomenon is not a "hard and fast" rule.

The majority of ctDNA would likely be (as you suggest) from lysed cells, however, should mutations occur that allow for the aberrant export of DNA, then the latter could occur (I would assume this is rare but based on the currently available literature this possibility cannot be discounted).

Thus your "new hypothesis" seems to be the most likely.