[...] mais ce n'est pas parce que personne ne se bat que le gens se sentent en sécurité pour autant.
The pour autant can often be rendered in English by just because.
[...] but just because no one is fighting does not mean people feel safe. For me, in this case the pour autant qualifies the whole thing.
Pour autant is a phrase. In a more formal text (not speaking), it can be rendered as merely because. In English, though complicated, the because is a preposition. And here is a link explaining it: because as part of a preposition phrase: http://languagelog.ldc.upenn.edu/nll/?p=9494. I submit that in French it is a functionsfunctions more or less the same way but is often placed at the end of the argument presented.
Please note that dictionaries translate it as: for all that. In some cases, that works but not so well here.
It also is a discourse marker in French that restricts an idea: http://monsu.desiderio.free.fr/atelier/lienslog.html
Tu devrais étudier d'avantage mais pas te fatiguer pour autant.
You should study more but you needn't tire yourself just because you do.
Sometimes it only qualifies the possible outcome, unlike your example.