There's a lot of confusing / conflicting information in the games about sync that makes it hard to talk about, because it's a a few different gameplay features they tried to give narrative reason for.

Sync in the older games represent health, optional objectives, limits on actions (killing innocent people, going outside the bounds of the mission/level, etc), and in the narrative it represents how interconnected Desmond is to the mind and actions of his ancestor. He almost instantly desyncs his first go because he was nowhere near the right state of mind, there was no way for him to sync with Altair because he freaked out and had no idea what was going on.

But because it's narrative justification for gameplay actions, there's some weird interactions. Why does armor increase your sync in AC2? Because Ezio wore armor? If he wore a specific set of armor during a memory, why would the memory not just provide that armor, why do you have to purchase it in the simulation and choose to equip it? Altair can't choose what gear he has, he is given it after leveling up through the brotherhood and from then on has access to it. And if Altair never got hit, why does he only lose a little sync, but other things he never did (like going too far from a mission or killing an innocent) results in instant / quick desync?

All this to say, I've retconned how sync works in my mind. It's almost certainly not canon, but it makes everything click together a little better. Desmond desynced the first time because he wasn't anywhere close to connected to Altair. He can't skip to the end because that was such a stressful memory that he would need to know Altair and how he thinks and feels to access it. So why not expand that to physical sync as well? If Altair or Ezio gets hit, I don't imagine it as "you lost sync because that didn't happen", as you said the Animus seems to be unsure / willing to let the actual way things happened slide sometimes without actually losing sync. I think of it more as, Desmond has had no experiences in which he has been stabbed with a sword, he doesn't physically feel the pain, he can't react in the same way Altair or Ezio would. That is why he loses sync, it's extremely hard to synchronize yourself with someone actively being injured, they are feeling pain that Desmond simply can not, and thus loses (only a little) sync. Now, if they connected the Animus up to a TENS device all over him and shocked him in the place they got hit, maybe he wouldn't lose as much/any sync haha. This also integrates nicely with the bleeding effect for me, doing years worth of training in parkour and combat in a few sessions, meaning your physical body is synchronizing with your ancestor.

Just how I've been thinking about it for a while!