It may be true for first time NM licenses, but it is also if you want one of those federally compliant drivers' licenses that certify that you are a citizen and allow you travel on airplanes.
For males, it just means you just bring your birth certificate. For females who have been married, it is much more of a hassle, because you have to provide certified proof of each name change, i.e., certified copy of marriage certificate. This has proved a big problem for many older women who may have been married multiple times, especially if they don't have certified copies and/or the state in which they were married back in the mists of time can't find the certificate (courthouse burned down, docs lost in flood, etc.). It can also get very expensive. There are other problems, such as that you cannot use your maiden name as your middle name, or the initial of your maiden name, even if that's how you've been known legally forever, unless you do a formal name change (expensive hassle).
If you can't find or get all that stuff, and you are already a NM licensed driver, you can just renew your old license, but it won't be one of those federally compliant ones.
Big fat hassle.