HPLIP correctly installed but hp-setup will not run - asks me to install hplip

Question

I am using Ubuntu 16.04.

I have installed HPLIP from the Ubuntu repository using the command sudo apt install hplip hplip-gui as recommended in How to install HPLIP on my Ubuntu to support my HP printer and/or scanner?.

However, when I run hp-setup I am told to install HPLIP.

The program 'hp-setup' is currently not installed. You can install it by typing:
sudo apt install hplip

This is circular since I have HPLIP already installed. Can anyone suggest what I should do next?

Output of sudo apt install hplip:

Reading package lists... Done
Building dependency tree       
Reading state information... Done
hplip is already the newest version (3.16.3+repack0-1).
0 upgraded, 0 newly installed, 0 to remove and 27 not upgraded.

The output confirms it is installed.

Output of dpkg -l hplip:

Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name                        Version            Architecture       Description
+++-===========================-==================-==================-===========================================================
ii  hplip                       3.16.3+repack0-1   amd64              HP Linux Printing and Imaging System (HPLIP)