UPDATE 2: Firmware version 47.1.A.5.51 has the fix! Note that you'll have to manually enable distortion correction in the camera app settings, it's disabled by default for some unknown reason.
Just replaced my Z5C today with a brand new XZ1 Compact. It's a mixed bag for sure, with some improvements and some steps backwards (no FM radio, double tap to sleep/wake...), but the worst thing I feared is the same camera distortion issue first reported by XZP users, and unfortunately it's bad news.
The XZ1C main camera takes distorted pictures as well. Boo!!!!!
FW ver: 47.1.A.2.324