It’s a real thing, pope Benedict allowed Anglican parishes to come over wholesale and retain the Anglican “Sarum” rite. My limited understanding of the situation is that our lady of atonement is an outlier in that she is an anglican rite parish, but not in the Anglican rite Ordinate (which has its own Bishop). Because of this they are under the legal authority of the diocesan bishop. However, my understanding is that they applied to be switched over to the Anglican rite ordinate before this latest move by the Bishop.
We need a “brief” on the Anglican/Catholic situation! I am seeing a half dozen “Anglican” churches/diocese sites in the San Antonio part of Texas. Some have a Nigerian bishop/connection. Some background from a “FR Anglican Expert” might be in order. Thanks! ;-)
http://church.atonementonline.com (The church in question)
http://epiphanyanglicansanantonio.com
http://stjamesanglicancatholic-satx.org
http://www.allsaintsanglican.net
http://dioceseofthewest.org
http://www.anglicancatholic.org/frequently-asked-questions
http://anglicanchurch.net