Regardless of what is causing this it's evident that bonding the inverter's output makes this "problem" of errant voltage readings disappear ... whether that's preferable or not I guess is the question I still haven't been able to answer.
I believe the several posts that have put forth an opinion have agreed that (1) It's not a problem, and (2) There's no strong argument toward bonding or not bonding. IMO, there's no strong argument because it's not a problem. For myself I wouldn't bother bonding it, but if it makes you more comfortable, add the bond.
A lot of debate on this thread:
406 posts about floating output, grounding, and bonding.