Question from Kymberly - Pope Pius V in Elizabeth I's reign

Hello! I am merely a curious person who wonders if Pope Pius V realized the pickle he was putting Catholic subjects in during the reign of Elizabeth l. Was he aware? Did he care? History suggests Elizabeth herself preferred to live and let live, and her actions prior to the bull establish that. The edict against her seems a logical explanation for her change in policy regarding her Catholic subjects. But is there any reason that can excuse Pius V's risking lives not his own, lives of those who were even sympathetic to his beliefs? Am I looking at Pius V through too modern a lens? Was he in emotional competition with Elizabeth, desiring evidence of greater deference to himself over the Queen of England? Are there any surviving documents that explain the pope's decision to place other Catholic lives in such peril? I am sooo curious! Thank you! Sincerely, Kymberly