Dave apparently didn't play the clip far enough.
Comparing the first section to your clip with the guitar, the hiss was at about -47dB. The hum part was about -40dB, so 7dB of additional noise. The guitar section peaks at about -4. But, the hiss is clearly audible. I'm not sure where that is coming from, the ZED, your guitar, your volume settings (improper gain staging), pedals (do I hear a bit of a compressor? The hiss seemed to pump a bit).
The hum you are getting when you don't touch the guitar shouldn't ever be an issue, as you HAVE to touch the strings to play the guitar. The hiss, on the other hand, is a bit of a problem, although with a full band playing, most people wouldn't notice it. But people who listen for that stuff definitely would hear it. ~43dB S/N isn't a very good level.