Did CAFTA Cause the Honduran Coup?

That's the allegation of a post at Eyes on Trade:

The situation in Honduras has a number of important implications: Fair traders have long argued that NAFTA-style deals promote instability and now Honduras, a signatory to CAFTA, has suffered Central America’s first coup since the Cold War. CAFTA was approved in Honduras by local elites, the same interests who are threatened by Zelaya’s progressive policies. The instability in Honduras is an illustration of how NAFTA-style trade agreements can undermine democratic governance in member nations.

What's the evidence for this claim? Honduran "elites" supported CAFTA and opposed Zelaya's populism, so obviously the two must be linked.

Except... not so much. Zelaya was deposed because he wanted to alter the Constitution to allow himself to stay in office. Honduras' Congress, Supreme Court, and even Zelaya's own party (Partido Liberal) opposed this move, and it was ruled illegal. Zelaya was undeterred and scheduled the referendum anyway. So the Supreme Court ordered the Honduran military to remove Zelaya from office (and from the country). There is no indication that this had anything to do with CAFTA.

Ironically, one of Zelaya's biggest supporters since the coup has been the United States, a CAFTA signatory. Oh, and Zelaya himself was a "vocal proponent" of CAFTA, much to the chagrin of Latin American leftists. And the U.S. and Dominican Republic are considering using CAFTA-legal sanctions to force Zelaya back into office.

Zelaya's ousting had nothing to do with CAFTA, and CAFTA might actually help him get back to power. This kinda undercuts the argument that "NAFTA-style trade agreements can undermine democratic governance" doesn't it?