There's a pretty clear correlation between specific genes and EDS, and there's a pretty clear connection between EDS and chronic lower back pain ("cLBP" in the study). There's a connection between EDS and "psychological distress" noted, but the authors seem to indicate that EDS is causal in both the psychological distress and the cLBP, not the other way around. There's no noted correlation between psychological distress and cLBP. On the contrary, it seems like psychological distress and cLBP are actually correlated with different variants of EDS.
"Is back pain in an EDS patient caused by stress?" is a valid scientific question, but it's not one that's likely to yield any interesting results if you test it, because so far I see no evidence, even anecdotal, that the two might have a causal relationship. There are higher-priority questions to investigate that are more likely to yield interesting/productive results.
