Having installed the various HPLIP devices and detected/configured the printer, trying to run the bundled installer:
The "hp-setup" utility silently fails to download the proprietary scanner driver from hplip.sf.net - so I needed to browse to http://hplip.sourceforge.net/plugin.conf and manually download the correct-version ".run" file from http://www.openprinting.org/download/printdriver/auxfiles/HP/plugins/hplip-3.10.6-plugin.run , manually specify the downloaded file's location, and I had to make sure I was root (using sudo) when running "hp-setup".
This brought me to a state where the hp-toolbox utility could see the printer (and the print drivers were installed).
Attempting to run "hp-scan" exited with "error: SANE: Error during device I/O (code=9)". Other scanning attempts with hp-toolbox bombed out with a GUI dialog "Failed to scan" "Unable to connect to scanner" and console output "** (simple-scan:3837): WARNING **: Unable to get open device: Error during device I/O"
I found the solution here: https://answers.launchpad.net/hplip/+question/18354 which involved going to /usr/lib and making a symlink named libhpmud.so to libhpmud.so.0 :
$ cd /usr/lib
$ sudo ln -s libhpmud.so.0 libhpmud.so
Now scanning works.