Турнир "ФБ-6" -> Tournament "The Final Battle - 6"

Stop trolling. I encountered desynchronization issues long before I even heard about Total Enhancement (TE), and HD Mod wasn't even a thing yet. Now I mainly play TE (with the Victory Tournament patch), always with a mod, and I haven't experienced desynchronization in about two years.
You can only talk about a connection between desynchronization and TE in relation to TE-Lite (which hardly anyone plays anymore); there, desynchronization is indeed abnormally frequent.

You're the one trolling. :)
You're talking about yourself, but you appeared in the Heroes world three years after me – on Heroes Paradise in 2007. ;)
Even when I appeared in 2004, TE already existed.
Therefore, it's quite possible that you were a newbie playing with someone who had both SOD and TE installed, and you experienced desynchronization.

In my opinion, the guys have a very clear situation that explains the nature of desynchronization – it shows that Archangels sometimes kill one Angel and sometimes three.
But this is fundamentally impossible!
Archangels have a constant damage value!
I think that one of their versions calculates damage differently, and when the data is transmitted, the other receives inconsistent information, resulting in desynchronization.
IMHO, this could be an explanation.

Medium, if you have facts/logic, then speak, but just saying that your experience says something... that's not indicative and there's no need to insult anyone. It would be better for everyone to understand the nature of desynchronization.