Mystery solved! Seems that elementaryOS uses Flatpak when installing applications from their AppCenter, and Flatpak installs are very sandboxed. So sandboxed, that the web browsers wouldn't even open files directly from a USB stick. I installed the binary directly from the Mozilla site instead (ie the .tar.bz2 file they suggest by default), and I can open my local index.html file on the USB stick just fine now. So I think my Linux lesson of the day is - Don't Use Flatpak!