Synthetic control, exogeneity of treatment, parallel trends assumption? I am relatively new to methods for causal inference. So, please excuse my conceptual confusion. However, I have been looking into the synthetic control method first proposed by Abadie and Gardeazabal (2003) in this paper on the economic costs of conflict. One thing that is confusing to me is that in most of the papers I have read the treatment does not seem to be exogenous. I understand that the Basque region presents a unique opportunity to study the economic costs of conflict since the terrorism there unlike in some other places was not economically motivated. However, it still seems to me that the onset of terrorism was not random by any means and that in turn there could be some other confounding variable effecting both the onset of terrorism and GDP.
How do we know that there are not violations to the parallel trends assumption? Would anyone be able to explain this to me? My understanding is that like difference in differences designs synthetic control methods still rely on the parallel trends assumption for causal inference. However, if for difference in differences designs the treatment needs to be exogenous for the parallel trends assumption to be satisfied. Why do treatments often not seem exogenous when synthetic control methods are used and there is seldom an explanation of why the parallel trends assumption is satisfied?

Unlike the difference-in-differences, SCM does not assume parallel trends. It allows for the effects of observed and unobserved predictors to change over time while assuming that pre-intervention covariates maintain a linear relationship with outcomes post-treatment (see p. 399-400 in Abadie's JEL paper for a comparison of the two). This is a much weaker assumption than parallel trends.
This explains why economists don't spend any time worrying about this, except to show that it fails and they cannot use DiD (e.g., see p. 397 on the paper linked above).
