it sounds to me like all your buttons are permanently grounded. If you tried against a completely clean OS, one that you are sure does not have any service or dtoverlay applied then it is likely a fault with the pHAT BEAT.
That said, try the below first:
1) disconnect the speaker(s). You don't need sound output for these tests.
2) start the Pi and after loading the daemons the VU should flash once.
... if the VU does not flash, that may mean the
phatbeatd daemon is not running, though that wouldn't explain the problem. Try:
sudo service phatbeatd restart
the buttons should affect volume and the VU will reflect the volume change (you can confirm the level via the web interface however, if you want).
If that sorts it out, reboot the Pi, again without speakers connected. If the button do not function again, then you need to check what is going on. try:
sudo service phatbeatd stop
sudo apt-get install raspi-gpio
sudo raspi-gpio get 26
try with and without the 'volume down' button pressed. the state should change, otherwise there is an issue with the button. You can repeat the above for each button. See the relevant bcm pin numbers here:
... this should give you an idea of whether the problem is hardware or software. In the former case then you'll need to contact support for a replacement. If the buttons work correctly however then post as much info gathered through herein troubleshooting steps and maybe we can figure it out together.