If that is true, no wonder it doesn't work right. I know the basics of capacitance touch screens, and I would have never thought there would be any way to distinguish to any degree of accuracy between one person's finger and another.
Visually yes. But with variations in the capacitance charge of people's fingers? I don't see it.
https://www.macworld.com/article/2048514/the-iphone-5s-fingerprint-reader-what-you-need-to-know.html
A capacitance fingerprint reader leverages a handy property of your skin: The outer layer of your skin (your dermis), where your fingerprint is, is non-conductive, while the subdermal layer behind it is conductive. When you touch the iPhones fingerprint sensor, it measures the minuscule differences in conductivity caused by the raised parts of your fingerprint, and it uses those measurements to form an image..
The article says that the capacitance reader has a resolution of about 500 dpi - though it uses the home button, not the screen.