She has a RealID TX driver's license. (She'd gone by her maiden name for various reasons, some professional, until she bailed on her previous profession and didn't want to be linked to that public profile.)
The marriage license, I believe, got her a free court document that showed her name change. (It was cheaper than petitioning the court for a legal name change, and also provided the reason for it in a culturally appropriate way that brooked no possible complaint or contest.)
The SAVE Act refers to and ID issued under the documentary requirements of the RealID Act and then adds free-standing documents which are to a fairly large extent (but not entirely) a repeat of those documents.
The RealID requirements include
Where a State permits an applicant to establish a name other than the name that appears on a source document (for example, through marriage, adoption, court order, or other mechanism permitted by State law or regulation), the State shall require evidence of the name change through the presentation of documents issued by a court, governmental body or other entity as determined by the State. The State shall maintain copies of the documentation presented pursuant to § 37.31, and maintain a record of both the recorded name and the name on the source documents in a manner to be determined by the State and in conformity with § 37.31.
Note that the Ms Magazine complaint about married women (at least those that changed their name on their IDs in a non-RealID-compliant manner) also applies to various other groups of people.
More to the point is the argument that there are some states, years later, that still find re-issuing drivers licenses and other forms of ID in a RealID compliant manner to be onerous. The gripe is always that it would be too expensive and difficult to re-issue them quickly--but they've had over 20 years go do this. The other argument is that not everybody can afford (over a 20-year span?) to get a copy of their BC or other birth documents. (And even then, there are ways to avoid that barrier.)