Petrice's followers are zealots - they don't need evidence to believe what they want to believe. Or many of them are very easily swayed with very little. The chantry hardliners wanted the Quanri villified, and they didn't care how it was done. The murder of a chantry sister will demand a full and proper investigation. Gangs will be keen to say it wasn't them, and the zealots could use that easily to their advantage. 'Say it was the Qunari and we lay off you' etc etc. But even just the suspicion will do - she was trying to address the Qunari 'threat' and she ended up dead. That's all the connection most will need. The Arishok himself muses with exasperation that even though he has done nothing provocative, the zealots have continually harassed and attacked them. This would be no different - Petrice's own philosophy was that 'a death' was needed. She doesn't want that death to be her own, but if she did die, her supporters would see that this 'opportunity' was not wasted.
Like it or not, even in Act 1 her status as a sister makes her very much 'someone', which she wastes no time in letting you know. Her death would not go unremarked even at this stage. The faithful are already looking for ways to excuse acts of aggression against the Qunari - she is simply one of the most daring and scheming. Killing a holy woman is no small matter, and no small crime. The idea of killing a chantry sister in cold blood (no matter how snide and conniving she is) would not sit well with most of the party. Because they'd either have severe moral objections and/or not want the massive amount of trouble that will land on them if it gets out. Killing people like Javaris is very different to killing someone like Petrice. Javaris was a greedy fool who dealth with cut-throats and bandits on a regular basis. He was a small time nobody of a merchant, who nobody would miss (Varric doesn't really know much about him, and Varric knows all the merchants and members of the city's underclass who matter). Petrice is a holy sister, advocating resistance to the Qunari in a city full of chantry supporters.
Its like in LA Noire, when Roy Earle takes you to see Mickey Cohen, the local mob boss. Roy is fairly candid that up until that point, the cops didn't much care what cohen was doing, because only blacks and small time crooks etc were being hurt (a terrible attitude, and not mine obviously). But when important white people started dying, then the cops have to be seen to be taking a stand - hence the visit to get Cohen to stop. If Petrice was to be killed, it would cause outrage, and the guards would be under pressure to find out who did it. You can well imagine that mahy would not be sorry to see the Qunari implicated, and make them a scapegoat (and frankly you'd have dropped Aveline right in it, if she was there when you murdered Petrice!)
As for witnesses, how do you know there aren't people watching? You didn't know Ser Varnell was about when you first meet Petrice either (i,e she was never really in any danger from those robbers). She and Varnell could very well have other men waiting in the wings - for all you know, she paid the gang you fight to create the illusion of a damsel in distress. I wouldn't put it past her.
Whichever way you slice it, Petrice's status as holy sister means that your killing her would be an act of suicidal stupidity. Unless you can prove she did something, you can't arrest her. And frankly, unless she comes at you with a knife or something, there is no situation in which killing her could be justified. The reactions of your party members make it plain that they consider her a utter ******, but they don't advocate murdering her for it. .