You over-analyse, I feel. In short, the execution of Eturrer was met with mixed levels of criticism and a good deal of approval.
This is because the most idealistic in the Federation's population rightly feel that they were all above that level, better than enjoying a public execution, no matter who it was. The rest felt justified and a sense of karmic retribution was had - after all he betrayed the Union itself and the Union, far as people seem to believe (at least I got that impression from PF) IS THE PEOPLE. He stabbed down everyone, for his own gain, and sold them out to their self-declared enemies. So they all had a hand in lighting him on fire and watching him die. It's a tad hard to get more eye-for-an-eye than that.
I also feel that much of the flak the Fed got for this, whoever it was from, was a good 50/50 mix of IC opportunism and OOC bias - there are so many characters out there who detest the Fed and would waste NO CHANCE WHATSOEVER to smear them, and making a crying face over the Eturrer execution is easy enough to do, even if the ones making the sad faces are Angels, Guristas, Sansha's and more and frankly have no grounds to speak on such matters. They will anyway, because that's how characters, just like humans, work.
The OOC bias comes from the OOC shock of "wait did the Fed just burn him alive on stage? That's barbaric, I did not expect they would be capable of such a thing! How could they do that, that's horrible!" and so many pro-Fed toons made a point of stating how horribly wrong they felt it was. I got the feeling at the time that only a few of those were even IC, based in what I had seen from the characters in question in the past.
Ofc, my own toon, being the unforgiving twat that he is, loved it and felt it was perfectly justified. OOC, *I* also liked it as it demonstrated a blacker part of the Fed, and demonstrated what happens to you (or more likely, COULD happen to you) if you betray the Fed from to high a position. Eturrer was crisped on stage for being the supreme commander of the Navy and selling the people out. A cadet in the navy doing the same would only be imprisoned and possibly shot for the same, if only because said cadet could not manage to let his/her betrayal have to large consequences.
And then ofc in the end there are the characters who hold Eturrer's execution up as a 'standard' in the Fed, something that happens all the time, if you believe the rhetoric, and something that invalidates any Federal right to complain about anything done to themselves. This is ofc as accurate and 'right' as Amarrians having no right to complain about, say, Matari terrorists slaughtering their people because 'herpaderp, you bombed a whole planet to dust once.' The situations are different and the conditions are completely different and the reasoning is totally different.
But that kind of logic has never stopped anyone.