Nope, sorry. You’re still presenting incorrect information, so you don’t get the last word 
Try reading up on it eh? Wikipedia is your friend
Your ping is only related to the “speed” (you mean bandwidth btw, not speed) of your connection if the size of the data you’re sending is greater than the bandwidth you have available. If each packet can successfully be sent without exceeding the bandwidth available to a single packet, there is no implication for latency related to bandwidth. If you can’t fit the data for a single packet within the bandwidth available, then bandwidth is your problem, not latency - and it’ll be impossible to play that game on that connection. You did get one thing right though - the main cause of latency is the distance between you and the server, with the number of “hops” along the route also being important.
Your original point is still faulty though - high ping in any game makes precision more difficult. Every FPS since QuakeWorld (not Q1) has used client prediction code in an attempt to ease the problems caused by latency, but they simply cannot be removed completely. I don’t think you understand how network transmission works at a technical level - because if you did, you would not have made the statement that “headshots are ping dependent in Brink”. You can apply judgement and experience, and luck will always play a part - but precision is ping-dependent regardless of the situation or game, and it cannot be avoided - only eased.
If you find headshots more difficult in Brink that ET:QW, that’s going to be down to things like hitboxes, weapon spread etc. If ping was really a problem factor there, it would also be affecting shots landed in other areas too - so some of your torso shots would also be unexpectedly missing. Shot detection will be the same for the entire body, it’s just that the head hitbox is obviously smaller. You mention only headshots, so either you’re not looking at your evidence properly, or you simply have the wrong end of the proverbial stick - or a bit of both 