Whether it's designed for use with a phone (or other portable source) is really not the point, IMO. Any electronics that use mains power should have sufficient grounding capabilities, and this is especially true of those that ship with an external power supply. Since the Zen DAC doesn't ship with a dedicated power supply, I think the next steps would be to try another power supply (maybe an iFi iPower2, if possible) and to contact
@iFi audio directly regarding the grounding issue.
@danny87 - Have you contacted iFi support regarding the grounding issue?