The definition of spouse for immigration matters is indeed a federal matter. The fact that they have a cohabiting partner visa should indicate that they feel there is a difference, "full faith and credit" notwithstanding (hows that for a constitutional mixed-metaphor).
While a J2 I-94 was issued by CBP, as you mention the CIS issuing the EAD will be a different matter.
Since, by reg, a J1/J2 is not even a resident of US (remember to keep filing your
taxes in canada), it may be difficult to rely on the common law rules of a state in which you are not considered resident to establish your marital regime.
All the best.