Would anything be different if the girl had been in there getting raped and murdered at the time and they saved her?
Sure you can call the police but they may be too late. Without probable cause they may not get in at all.
As already covered, someone "going vigilante" runs the risk of being wrong. If they're right, they'll probably only be given a slap on the wrist on the legal side, and be hailed as a hero by many. If they're wrong, they'll be vilified.
So IF the girl had truly been there, their story would likely be different. But she wasn't, they were wrong, and they're being vilified. It just also happens to come with the added onus of it becoming a "white on black" racial incident in a region with a history of such things, so it's even worse for the vigilantes in this case.
Now if the girl had been in the house, was being raped, and someone in house opted to "stand their ground' in defense of the house, I think their legal defense would fail as most juries would instead conclude they were acting in defense of a crime, not defense of their home. So any vigilante they kill during that confrontation would result in their being prosecuted to the fullest extent of the law--for killing the vigilante.
"Vigilante justice" where it interfaces with the law is a very grey area with all kinds of bizarre and twisted permutations that can come into play.
You need to also remember that the legal code itself can make some strange turns in regards to
otherwise legal behavior when it happens in connection with a crime.
See: Getaway car driver.
There's nothing illegal about picking someone up and driving them from point A to point B while properly observing "the rules of the road."
Unless you knowingly picked that person up after they robbed a bank and you're helping him transport the goods to somewhere safer.