Um, no they don't.
From my understanding of the article this isn't a function of state law.
The family purchased a bunch of plots in a private cemetery and one of the provisions was that an individual has to be legally married to qualify for a spousal position in the plots to be buried next to a spouse. It's not a state law, it's basically a "trust" administered cemetery administrators. The spouses involved are legally married, just not under the laws of Ohio, however does the plot trust state that the marriage had to be performed in Ohio?
I think there are a lot of spouse burials in Ohio where the participants didn't enter into the Civil Marriage in Ohio.
Ohio does not recognize homosexual marriage nor civil unions. I am not surprised that the state is fighting back on this one. They should. They went to Maryland to get married in order to try to circumvent Ohio law and Ohio shouldn't contest the ruling, which I think was a bad one. I think Ohio will win this case.
You can't reason anyone out of a position they didn't reason themselves into in the first place.
Sure, the marriage license was issued by the state of MA, I'm sure MA recognizes their own license.
If Ohio doesn't recognize it? Who cares, the issue has nothing to with them unless it's a state run cemetery. They quys have a legally valid Civil Marriage licenses and therefore one is the spouse of the other.