Read the article. The terrorist group wasn't tangentially related to the organizations she belonged too, they were "affiliated." As in, "officially attached to or connected." Not "oh a few people were in both groups," like many people are suggesting. The article doesn't explain the connection, but presumably they were all of the same blanket organization. She visited a convicted terrorist from the group in prison, suggesting that she knew the terrorists and was in an organization that she knew was connected to terrorism, even if she herself did not assist with any terrorist acts.
Knowing terrorists and having been tangentially involved in a terrorist organization is not in itself a crime, but yes without a doubt that is something she should have disclosed. Essentially, she lied on her background check and got fired. Good.
Of course not everything should be asked on background checks. I think it's fair to say, sexuality shouldn't be asked, or political affiliation, or a number of other things. The potential for abuse is too high. But if you can't ask employees if they have a connection to terrorism, what are background checks for at all?