I'm not trying to argue that your stats aren't correct. The problem is bad enough that 3rd party CS matchmaking services like ESEA force you to run additional anti-cheat clients on top of VAC.
However, hand in hand with cheats existing is excessive accusations of cheating. When I used to play CS:S a lot, I would regularly get banned from servers for "cheating", because I would completely legitimately pull of stunts like shooting people in the head through walls with single shots from an M60, because players are predictable and headphones can be great at pinpointing player locations... i.e. a lot of smart play gets accused of cheating. Like I said, this kind of play is at the point in CS:Go now where I've been vote-kicked from competetive matches because I wasn't pre-aiming at targets properly before they appeared. The current meta-game is pretty harsh.

you cant know where some one's head is before you've seen them

Just to make this clear, even without cheating, pre-firing is an expected core skill of the game -- you are expected to be able to shoot at an enemy's head before you even see them, without cheating... just by intuition and practice. That's how broken CS's meta-game is. This is not a game that feels fair when played by decently skilled opponents. It feels bullshit by design :(
Now add to that the fact the CS:Go is straight up broken a lot of the time -- for example, the fact that one-way-smoke exploits are a feature, not a bug -- and that it's community is horrendously toxic, and that cheat-like stunts are commonplace game mechanics, then spurious accusations of cheating are going to be far more common than cheating itself... even if cheaters are as high as 5% of the player base as your data suggests :o
My personal solution was to simply give up on the competitive mode and only play the casual CS:Go modes :D

This kind of fight-fire-with-fire tactic is pretty awesome though. It could be worthwhile to employ someone full-time to write cheats for your own game, simply so you can detect them... I know a game developer that defeated crackers for their game in a similar way -- they most of their piracy checks were time-locked and/or added in patches. This meant that all the cracks for the game only work on the first version and require you to not play online. Also, the crackers kept losing their dignity / street-cred by releasing a crack that worked at the time, but stopped working a few days later. The company CEO would hang out on the cracking forums (pretending to be one of them) and would rile up the crackers who kept faililng to produce a reliable crack. Eventually they got pissed off enough to say "fuck that game" and stop trying :lol:

Other solutions involve changing the gameplay... IMHO, everything that I've said above is evidence that CS cheating is at the root of it, a game-design problem.
A game that features one-way smoke, has developed a meta-game where pre-firing is an expected skill, and one where twitch reflexes and 180º headshots are more important than tactics and strategy...? That's a game designed for esoteric e-sports heros, not us mere mortals, and also one that's very hard to detect cheating because pro-level play looks exactly the same as the play of a robotic cheat program.
Design shooters that emphasize strategy more than precise mouse flicks and cheats become less effective.

At the other extreme is running the entire game on the server, and only streaming MPEG to the user's PC :lol: Then cheats will have to do machine vision calculations in order to work... hopefully making them computationally infeasible for a while... This is basically how big tournaments are provably fair -- you have to use a provided PC instead of your own PC and only bring your own peripherals, so any cheats would have to be written into your keyboard/mouse firmware.

Anticheat isn't scanning your machine for other programs, even if it was it wouldnt have a clue what they were doing. You can run screen capture with framerate overlay and it isn't flagged as a cheat.

Lots of anti-cheat software does do that. If you buy every cheat available and add it to a database, this is an easy way to detect them. Screen capture programs are often specifically white-listed so as to not be flagged as cheats. Some also take screenshots, stenograph private information into them, and upload them secretly for analysis.

I no longer have the time to play and be remotely competitive in games like this, but there was a point where I could often get kicked from CS:S games for 'obvious wall hacks' and 'aiming through smoke'.

Detection on people actually cheating, vs people who are highly skilled and using every advantage they can is not a trivial task. CS:S has multiple features built in that let you follow people through walls with surprising accuracy.

1. Sound: I've seriously been surprised at the number of people who call out "HAX!" on someone following a user who is on the other side of a wall because they're listening to the other user clomp around while running at full speed...

2. Timing: Maps are small, and played in an extremely repetitive manner, with the majority of players consistently rushing to the same positions at the same speeds each and every game. Play enough rounds, and pay enough attention, and you can begin to form a statistical probability map of where players are for any given time. - Combine that with all characters having their head at one of 2/3 heights off the floor 99.9% of the time...

3. Shadows: Has been awhile, so I kind of forger which titles I played had them and which didn't, but it was amazing how often users forgot that characters cast shadows... And shadows gave positional information that others could use. "I was standing still, how did you know I was behind that paper thin wall if you weren't hacking!?" - "Your shadow was showing on the floor in front of you..."

Combine those factors of a real user's potential ability with a small 'fudge factor' in an aim bot, and you have something that is terribly difficult to reliably detect and accurately judge from the stand point of an automatic system.

My personal view is: Find servers populated by a group of people with similar skills and a strong moderation presence. Hang out, make friends, and play with the same relatively small group of people rather than seeking to play against the whole world. Yeah, you get to deal with hackers now and then, but their 'reign of terror' is generally short lived, and they're promptly kicked by a human mod. Even if they're just super skilled humans, I really don't have an issue with removing a player from a community if they are not making that community a fun and better place for the majority of users. - If that community is paying for and hosting the servers, then it is kind of their right to only let people who make the game fun for them access.

However, these days I tend to stick to board games. That way you can reach over and smack the mouthy one going on about your mother, and they learn their lessons.