I get the impression that this man has not heard of Opus Dei. I have always though they dwarf Jesuits in terms of influence. But my opinion might be a bit dated.
Actually, Opus dei are hardly 80 years old. I don't know why people think they are so powerful in the overall scheme of things. If they were, the church would be alot more conservative in worship and theological discussion than it is. Certainly they have nothing on Benedictines, Jesuits, Franciscans, Dominicans and Carmelites etc. Most catholics have never even met a member or even know about opus dei or its saints, including St.Josemaria. But you bet most have been influenced directly by or know about these five groups either at the parish, in schools, hospitals or common spiritual practices like the rosary and such. In contrast, virtually any catholic with more than a superficial familiarity with his faith knows very well the saints of these great houses including St Francis of Assisi, St Benedict, St. Dominic, St. Thomas Aquinas, St Catherine of Sienna, St John of the cross, St Teresa of Avila, St Therese de Lisieux,St. Ignatius of Loyola, St Francis Xavier etc etc. Many of whom are doctors of the church, not just saints/canonized,meaning they still exert influence on the church's thought and are authorities in their own right beyond their own religious houses. Which in turn means that their religious houses, as the experts/keepers of the teaching of these saints, influence the church's thought a lot.
Personally, I think the idea that opus dei is very powerful is fuelled by Dan Brown's books and by John Paul II's warm relationship with them and looking at them with favour. But he looked at many groups with favour,not just opus dei, including charismatics who'd been accused of being protestant because of their pentecostalist tendencies, pope John paul ii protected them and their way of life/worship, all that Benny Hinn stuff. He even protected one group that we now know with certainty was totally evil and cult-like, with sexual abuse, that Pope Benedict went after, immediately he became pope. John Paul II with his "new evangelization" protected and promoted all catholic ministries that claimed to teach and preach the gospel with orthodoxy and engage in works of charity, that was his way. He gave them all permission to operate without specific permission of the local bishop. This independence is why I think many think opus dei is powerful. They operate like a global "diocese" of sorts with their own bishops, much like a religious order, though they say they are lay,which would normally have placed them under the local bishop of whichever place they are at.
Now that a Jesuit is pope, I bet all the old Jesuit-papacy conspiracy theories have been revived and turned up a notch.