Eh, not really. Most half-decent businesses have a privacy policy/TOS that explicitly makes this a no-go, and would be grounds for a lawsuit if a company posted a customer's conversations with said company. It doesn't look like Historious has such a policy, so legally it might be okay, but it's still scummy IMO.
Posting your side of the story is fine, but using communications that are expected to be private usually isn't, and you should be able to correct the story without posting private info (we don't even know if the transcript that Stavros posted is true.. he could have completely made it up for all we know).
With all that said, it made me curious to look at the TOS for IMGZ, and... yikes... https://imgz.org/help/terms/