If someone told you another person robbed something from them would you go [...]
No. Similarily, if someone told me in person that another person raped them, I wouldn't start questioning them on the spot either. But in both cases, as long as both sides were strangers to me, I would not blindly assume that the accuser is right and act on it. It's not my job to punish people for crimes, that's the job of the legal system. And if the legal system decided that there's not enough evidence to rule that stranger guilty of theft, I wouldn't consider myself to be more capable of judging that.

Also, it's important to remember that the 2-8% figure is likely to not be entirely accurate because it only includes the allegations that were proven to be false. In comparison, the rate of rape cases that end up with a conviction is less than 1% of the total reported incidents. But nobody is claiming that only 1% of the total reported incidents actually happened. That would be highly inaccurate and misleading.