PTSD based on false memories Memory is not just static snapshots or video on a harddrive, but an active process. As such, it is possible to construct false memories (Brainerd &amp; Reyna, 2005). Some of these false memories can be very traumatic (Loftus, 1996).
There is a lot of research of false memories and PTSD, but most of it is concerned around the accidental implantation of false memories during therapy (for example, see discussion in Hyman et al., 1995), or asking if PTSD-patients are more prone to forming false memories (for example, Jelinek et al., 2009).
Are there any case studies of patients who did not initially have PTSD (and were neuro-typical or 'healthy' in other regards, too) nor experienced any events usually associated with PTSD, but developed PTSD based on a false memory?

References
Brainerd, C.J., &amp; Reyna, V.F. (2005). The science of false memory. Oxford University Press.
Hyman, I. E., Husband, T. H., &amp; Billings, F. J. (1995). False memories of childhood experiences. Applied Cognitive Psychology, 9(3), 181-197.
Jelinek, L., Hottenrott, B., Randjbar, S., Peters, M. J., &amp; Moritz, S. (2009). Visual false memories in post-traumatic stress disorder (PTSD). Journal of Behavior Therapy and Experimental Psychiatry, 40(2): 374-383.
Loftus, E. (1996). The myth of repressed memory: False memories and allegations of sexual abuse. Macmillan.
An answer I provided before on the possibility of recalling forgotten memories briefly talks about False Memory Syndrome and PTSD.  As stated in the answer,


  Memory is not fixed as it is very plastic


and as pointed out in the article you referenced (Hyman, et al., 1995), people are susceptible to creating false memories.

To answer your question on whether non-sufferers of PTSD can develop PTSD from false memories, MyPTSD.com states that false memories can be traumatic and Psychology Today mentions an article (Southwick, et al., 1997) which reported that false memories increased PTSD in war veterans; however, I cannot find any definitive study on non-PTSD sufferers developing PTSD from false memories.  I would say that this is for the reasons @ChristianHummeluhr pointed out in his comment


  ...for methodological and ethical reasons...


For the reason that false memories can be traumatic and has increased symptoms in PTSD sufferers, I would say that it is highly plausible that false memories could lead to PTSD.

As @memebrain pointed out in his answer — although not correctly termed — there are are various forms of trauma that counsellors, psychotherapists, etc. can suffer from as a result of their work, and the US National Centre for PTSD (part of the U.S. Department of Veterans Affairs) has an article about it.

The secondary PTSD mentioned by @memebrain is actually Secondary Traumatic Stress which


  produces symptoms similar to PTSD.


We as counsellors and psychotherapists are trained to be careful not to create false memories in their clients and


we are also told how providing therapuetic help can affect a therapist's mental health as indicated in my answer to Are psychologists more immune to psychological problems? and
All UK therapists (experienced and low-experienced) who are registered with the Professional Standards Authority are required to undergo Clinical Supervision for reasons such as this, and for other reasons in my answer to How do clinicians control for their own mental disorders? 




Research Article References

Hyman, I. E., Husband, T. H., &amp; Billings, F. J. (1995). False memories of childhood experiences In: Applied Cognitive Psychology, 9(3), pp 181-197.DOI: 10.1002/acp.2350090302
Free PDF available at ResearchGate

Southwick, S. M., Morgan III, C. A., Nicolaou, A. L., Charney, D. S. (1997). Consistency of Memory for Combat-Related Traumatic Events in Veterans of Operation Desert Storm In: The American Journal of Psychiatry 154(2) pp. 173-177.
DOI: 10.1176/ajp.154.2.173