Are marriages outside of the US even recognized for tax purposes?

I've been thinking about this for a while now, and I'm trying to figure out: A couple who lived in another country and married in that country come over to the US. One is a permanent resident, the other is here illegally. My thought on this is, if they are recognized as a married couple, the wife should be able to get a permanent residence simply by being his wife, and therefore get a valid Social Security card. Since she's unable to do this, I don't believe their marriage is recognized here.

Can anyone enlighten me on this? Can you point me to the area in the tax code that states that they are either married or not married for tax purposes? I've been going through the pub 17, to no avail....