Ac is full of people who cheat, and people who don't cheat.
They range from average players to "depraved cheaters".
By delaying each outgoing position update to the server you can give yourself a considerable "jump" on opponents. For example you run into a room and you have seconds where you can shoot them before you will render. You are still receiving everyone else's position updates as normal, only selectively delaying yours. You allow your outgoing damage data to be sent as normal. That is one possible explanation, and one that people abuse in the majority of first person shooters in some form of another.
In the instances where you appear to "dump a clip" into someone only to die and see them with full health, that is a product of clientside hit detection. On their screen and as far as the server is concerned, they were already well on their way to killing you even though you might be shooting them before they even are firing or facing you on your screen. You have to be suspicious of players where this happens more often then not. It's also caused by lag compensation, your connection to the server, the load of the server, in combination with theirs. So it's not always caused by people "manipulating" their traffic, but it can be.
Now the other aspect is TTK.
Cheats like no spread, no recoil, silent aim/aimbots/aim assists will increase your TTK considerably.
Just like good aim and positioning will increase your K/D. People have to realize that under normal conditions headshots are not as reliable at certain ranges as you think due to cone of fire. And even body shots will cause bullets to hit simply from the "spread" of the weapon. Even with burst firing. So if your aim was dead on, you had the jump on someone, and burst fired appropriately for the weapon you were using, and the other person seemed to never miss a bullet, be suspicious. If those suspicions compound over time against the same players, they are likely cheating.
AC will embed themselves into any thread relating to hacking to use downvotes, fanboys, and throwaway accounts to keep their charade going. That's what cheaters do.
Because the reason people like AC cheat is because they want to be considered "good" or "relevant", and if this community didn't feed into that, it would be like taking the heroin away from an addict. They are attention seekers, and compensating for something missing from their regular lives. Among other psychological explanations like poor upbringing, immaturity, depression, isolation, being gay in a society that they don't feel like accepts them, yadda yadda etc etc.
Daybreak seems to ignore AC for whatever reason, probably because you get ISIS-like cheating videos whenever the community upvotes threads saying they cheat.