faith-based = believing in the truthfulness of someone or something, e. g. the reported atrocities.

These are groups of people who are backed by a religion or belief system. They usually cite references from the Bible or another religious book or source, to justify their actions or statements.

faith-based is a technical term introduced in the last several years as another way of saying religious, or religion based. The term is used for things like:

faith-based charities
faith-based schools

The term became very well know in the United States during the presidency of the second George Bush because he allowed government funding to certain faith-based social service organizations.

HERE ARE SOME EXAMPLES:

"Mark Chaves, Duke University professor and director of the National Congregations Study, recently commented that the National Congregations Survey shows that the Bush faith-based initiative "accomplished so little." Comparing data from 2006–07 with the results from 1998 shows no increase in the percentage of congregations that offer social services, the proportion that devotes at least a quarter of an employee's time to such services, or the proportion that receives government funding to provide services."
http://www.christianitytoday.com/ct/2010/januaryweb-only/14-...

During the Republican Party's 2000 national convention, the Rev. Herbert H. Lusk II, heartily endorsed Bush for president in a satellite television uplink from his church. Since that time, Lusk has repeatedly advocated for Bush's "faith-based" initiative that seeks to fund church-run social service programs.

As the president was preparing to speak at Lusk's Greater Exodus Baptist Church on combating AIDS at home and abroad, the Associated Press reported that the church's charitable operation, People For People, has been awarded a nearly $1-million "faith-based" grant.
http://usgovinfo.about.com/od/rightsandfreedoms/a/bushchurch...

When President Barack Obama launches his version of the faith-based initiative Thursday, he will expand the mission to include abortion reduction and outreach to the Muslim world. He will also try to avoid the thorniest constitutional issues that beset the program for years under his predecessor.
http://online.wsj.com/article/SB123379504018650159.html

Why should any faith-based organization — Muslim, Jewish, Hindu, Buddhist or Christian — be forced to change its organizational identity and culture in order to receive public funds so long as those funds are used as they are intended: to deliver effective social services and not promote any religious beliefs?
http://seattletimes.nwsource.com/html/localnews/2008771642_w...

faith-based => based on religious beliefs

Nothing else, but their faith brought them there, the reason to come was based on their faith.

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Note added at 1 day2 hrs (2010-10-22 16:55:50 GMT)
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To dear Bernhard: Certainly.