Here is the exact text of the Vienna Convention on Consular Relations with regard to this issue.
Section 36:
"With a view to facilitating the exercise of consular functions relating to nationals of the sending State:
...
if he so requests, the competent authorities of the receiving State shall, without delay, inform the consular post of the sending State if, within its consular district, a national of that State is arrested or committed to prison or to custody pending trial or is detained in any other manner."
Do we have any evidence that Medellín asked for a consular officer? The Vienna Convention requires the accused to request it.
Also, even if the accused did ask for a consular officer, the the Vienna Convention on Consular Relations states this in the same section as above:
"The rights referred to in paragraph 1 of this Article shall be exercised in conformity with the laws and regulations of the receiving State, subject to the proviso, however, that the said laws and regulations must enable full effect to be given to the purposes for which the rights accorded under this Article are intended."
The document that outlines the rights of nationals in relation to consular privileges specifically states that the nation in question must have its own laws directly related to the Vienna Convention on Consular Relations in order for that part of the treaty to be effective.
Did the United States pass any laws related to the Vienna Convention on Consular Relations? If SCOTUS found none, as I showed in a previous post, then they do not exist.
So what treaty did the United States violate?
The Vienna Convention on Consular Relations and Optional Protocols