Well, by your reasoning, she is required to make it a public issue. After all, if she had refused to stand there, then it would have been sending a strong message about the future of the marriage. I see her being there as a way to minimize the speculation.
No, standing there is a deliberate action, not showing up at her husbands press conference isn't, unless you consider she has an obligation to be there.
As to it being a public issue, good grief, he's the Governor of New York with Presidential ambitions, resigning over both legal and moral misconduct. It's a public issue irrespective of what his wife does.