The crux of the matter is, there is nothing wrong with, and in fact media indeed should, ask questions of an organization in the US and UK that is a branch of a parent group that praises bin Laden and the Taliban. What are their views on bin Laden, al Qaeda, the Taliban, suicide bombings, and why?
Like most groups centered around similar ideology, JI activisty encompasses numerous charitable works, as well as work with hospitals, universities and in economics.
Other information about links can be found in "The Vanguard of the Islamic Revolution: the Jama'at-i-Islami of Pakistan" by Dr. Seyyed Vali Reza Nasr:
"Today there exist 8 Jama'at-i-Islamis: 6 in Pakistan, India, Bangladesh, Sri Lanka, Pakistan's Azad Kashmir, and India's Kashmir province, plus the United Kingdom Islamic Mission and the Islamic Circle of North America. "
Relations between the groups are conditioned by nation-state boundaries.
For more on the history of JI, there's "Jamaat-i-Islami: The Catalyst of Islamization in Pakistan" by Dr. Pooja Joshi.