Medellin's Interpretation of the Supremacy Clause
It's a framing issue. Medellin is often framed in terms of treaty interpretation. We delegated a certain amount of power over interpretation of the treaty in the optional protocol, and are no bound by that treaty delegation. While I have some issues with this, it isn't necessary prohibitive; at least in the domestic context this happens all the time, and it isn't terribly new in the foreign context.
But the ICJ is not really interpreting the treaty, but the Supremacy Clause. There is, as far as I can tell, no issue as to whether Mexico is violating the treaty, and no reason why the Supreme Court wouldn't have agreed in Breard and granted the Mexican nationals relief.
The issue was the adequate and independent state ground. Texas has a procedural rule that is not preempted by the treaty, per Wainwright v. Sykes where the Court held that the procedural default rule is a valid exercise of state procedural power and can bar the litigation of a federal right. Avena is basically trying to overrule Sykes, saying in effect that the Supremacy Clause of the U.S. Constitution should make the treaty overrule the state procedural rule.
The arguments for Medellin always frame this in terms of a treaty interpretation, and that the treaty should be interpreted to preempt the state rule. But that interpretation is not really interpretation of the treaty, but interpretation of what the Supremacy Clause has to say about the treaty.
This, I think, is problematic. Far more important than keeping the definition of the scope of our international obligations under domestic control is keeping the interpretation of our constitution in our courts.