The only child of working-class parents in Greenfield, MA, Stetson went to Harvard, where he was prosperous enough to live at the upper-crust and reputedly gay Adams House and drove an apparently new Buick. He got to know Bernard Law, also an Adams House resident, and Law introduced him to Catholic circles in Cambridge. Stetson became an Opus Dei numerary while still a Harvard undergraduate, and he got in early with the establishment of the movement in the US.
From 1983 to 2010, he was the secretary to the delegate for the Pastoral Provision, who for most of that time was Bernard Law. For 17 years of that time, he was also vicar for Opus Dei in Chicago, where he seems to have earned the trust of Cardinal Bernardin, who gave Opus Dei the responsibility for renovating a Polish parish, St Mary of the Angels, in the Archdiocese of Chicago. Following that assignment, Stetson became Director of the Catholic Information Center in Washington, another Opus Dei function. He was appointed to that job by Theodore McCarrick.
During the later phase of his career, rather clearly able to gain the ear of influential cardinals in AmChurch, he seems to have operated as a general fixer for the Pastoral Provision on Law's behalf, although it's worth pointing out that the Pastoral Provision nevertheless underperformed, to the extent that Law continued to press for a personal prelature for former Anglicans, broaching the idea in a formal proposal to Cardinal Ratzinger in a 1993 meeting.
His appointment as director of the Catholic Information Center in Washington is also something of a puzzle. As best I can tell, this is basically a bookstore with a chapel attached and a small paid staff. Law's successors as director haven't been monsignors. That Stetson would fall from secretary to the delegate for the Pastoral Provision and Opus Dei vicar in Chicago to bookstore manager is a puzzle and may reflect an understanding within Opus Dei of his actual abilities, especially after his patron Law's departure from the US.
My own exposure to him during 2011-12 and the runup to the erection of the North American ordinariate is that he erred profoundly in his assessments of the Anglican clergy at St Mary of the Angels Hollywood, and Jeffrey Steenson also erred, as far as I can see, in accepting those assessments. But as far as I can see, Stetson had little or no experience in actually running a parish in any denomination; he was always above that sort of thing in the upper levels of Opus Dei.
My perspective now, after almost six years as a Catholic, is that David Moyer, who did have experience with Anglicanism, running a parish, and serving as a bishop, had a much better sense of what it would take to make the St Mary of the Angels parish Catholic, and my impression from the remarks he made during his episcopal visit in early 2011 was that the place was a disappointment and would probably need to be extensively rebuilt or expanded to be a true Catholic parish.
I think he had it right. I'm not sure what universe either Bernard Law or William Stetson ever thought he was operating in. But I think this also says something about the upper levels of AmChurch in the 1970s, 80s, and 90s.