Beggar,you have read my mind.......so many accusations, illogical events and statements made by CTA and the Dalai Lama without substantial grounds all reflected something is not quite in order.
Since Dorje Shugden has been practised for over 350 years, and the practice has been passed down from Pabongkha Rinpoche to Trijang Rinpoche and to many high lamas who reside all over the world now, almost every single Sangha is a student of Trijang Rinpoche. Therefore, the laypeople (ministers) of CTA could very well be Shugden practitioners.
Look at Samdhong Rinpoche, he spoke out publicly soon after his term as Kolan Tripa finished. He said all he did as prime minister was to follow his Guru Trijang Rinpoche's instruction. That speaks volume as he is a well known DS practitioner himself, some more it was said he is an emanation of Dorje Shugden also.
Another similar case is the 101th Ganden Tripa, Khensur Lungri Namgyal Rinpoche, who jump camp to Shar Ganden Monastery right after his tenure as Ganden Tripa finished and made a public statement as well.
So there are many high lamas, and I am sure many sangha and lay Tibetan people as well, that they are all practising Dorje Shugden "secretly" when they are holding their "official" positions. And that they have not given up this sacred practice passed down to them from their lineage guru.
Henceforth, the ministers in CTA could very well be "underground" shugden agents!
Last but not the least, Dalai Lama was practising DS as well officially before the ban! Who knows if he is also practising it secretly still ? The "Bigger picture" theory still stands firm and sound to me!