There is no aim or suppression penalty to enemies that you're shooting

Why would there need to be an aim or suppression penalty to begin with? 

It would mean that the person who shoots first always has the advantage instead of the person who aims, burst, tracks or chooses their engagements better. Suppression and flinch penalties reward people for bad aim or bad engagements. 

Presumably you had an automatic gun that did equal or less than 25 damage per shot, or you wouldn't have been able to make 3 headshots without killing your opponent. At 30 meters you'd have a pretty significant advantage over the sniper, you shoot faster and are punished less severely for missing a single shot. Yet you failed at landing that last bullet granting you the kill, before the sniper could return fire.

I can't tell you why you were killed first, but the lesson here is that an advantage doesn't guarantee a kill, it simply makes it more likely.

So just because you got killed, doesn't necessarily mean that there's something wrong with the game. That said, there are couple of other fixes that I'd suggest:

1. The headshot multiplier for the base weapon, hollow point and synthetic point needs to be high enough to guarantee a reduction of the bullets to kill. 
2. The sweet spot mechanic needs to be removed. 
3. The bullet drop for snipers needs to be more severe. 
4. The range finder attachment needs a nerf. 

I think that point 1 would be a better way to solve the issue, rather than relying on flinch or suppression. You made 3 headshots, so I think the game should reward that. 

Points 2, 3 and 4 wouldn't necessarily change anything at 30 meters, but it would make snipers less powerful outside of the range of other weapons.