Sometimes, of course, when Catholic priests were suspected of plotting against the government of England, they were plotting against the government or the monarch. Not every Catholic priest or layman executed by the English government died as a martyr! And although English Catholic men traveled to the Continent to study for the priesthood and for the mission in England, they did not always agree about what that mission was. In the latter part of Elizabeth I's reign, there was division between the Jesuits and some of the secular, non-religious priests called the Appellants over the better way to deal with the issues of Elizabeth's excommunication and rightful authority as Queen in England--dividing spiritual and temporal authority, as it were. The Appellants wanted to appeal to the Queen for mercy, claiming that they were loyal to her in temporal matters while still practicing their Catholic faith.
William Watson, who was executed on December 9, 1603, exemplifies these two trends in a fascinating pattern. Because he had great hopes that James VI of Scotland, when succeeding Elizabeth in England would be ready to accommodate this more subtle distinction between the secular and the spiritual authority of the monarch, Watson met James in Scotland. When James did not accept this radical notion, Watson concocted the Bye Plot to kidnap James, seize the Tower of London, and establish a Catholic government in England.
Henry Garnet, one of Watson's Jesuit adversaries, found out about the Bye Plot and reported it to the authorities. Watson and his fellow conspirators were captured, tried and executed. Father Robert Parsons and the Jesuits who had been also negotiating with James and his new government, also hoped that their cooperation in reporting this plot would encouraged the government to ameliorate conditions for Catholics.
Ironically, Henry Garnet would later be executed for his role in the Gunpowder Plot in 1606--a matter more complex than Watson's direct plotting. One of the plotters, Robert Catesby, asked Father Garnet some "hypothetical" moral questions and Garnet warned him against rebellion and the taking of innocent lives; another Jesuit who knew of the plot confessed it to Garnet who told him to do all in his power to prevent it--so Garnet may have been protecting the Seal of Confession. James I was careful not to make a martyr out of Garnet; he was threatened with torture but only tortured once (unlike poor Guy Fawkes in 1605) and was hung until dead before the rest of the traitor's sentence was carried out.
Also, the investigation of the Bye Plot led to the discovery of the Main Plot, which connived to place Arbella Stuart (pictured above) on the throne after deposing James.