The implication with reducing the argument to that picture, is that somehow that character is warping in and out of existence between those points. Like you have literally 15% as many opportunities to shoot your target with 20 tickrate vs 128. That's not true in the least.
The tickrate is only affecting how often the server calculates new actions and happenings. So for example if you hit shift at 0.0001 seconds and I hit left click at 0.0005 seconds, those would LIKELY be within the same tick and effectively happen simultaneously. Higher tickrate makes that slightly less likely, but it doesn't affect things in any way like what the picture is showing. In the example of the picture, that character jumps and moves forward. The only calculation that is happening there is one for the jump and one for the forward momentum. So there would be a 0.05 second window AT MOST where you might have jumped and the server hasn't decided that you jumped yet, once it decides that you've jumped it's tracking that information 100% 'correctly' to you the player regardless of when you hit it within that tick, the tick is just when it's kind of screenshotting what commands its received in that 0.05 second window and executing all of them as they were received. So like, you jump at 0.03 seconds, it doesn't tick until 0.05, now the server says 'yes you jumped at 0.03 seconds' and sends all of that to everyone else, now EVERYONE sees you jumped at 0.03 seconds and all of them are tracking you 100% correctly, the period of time where that wasn't the case was 0.02 seconds between when you hit space and when the server ticked, effectively. Once the movement is going, there's no like stuttering on the servers end, there's no invisible ghosting where you can't be shot between ticks or anything asinine like that. The server is sending movement directions to people, not static images of where people are standing at every tick. If I hold W, the server is not going to be wrong, other players aren't going to be wrong, nothing is 'wrong'. The difference between 20 tickrate and 128 tickrate for the movement in that screenshot would be infinitesimally small, and it would only occur at the exact moment the player hit spacebar to jump. You would never miss your shot because of it. the Latency of the internet is vastly larger than the slight difference in tickrate, for example.
Obviously a faster one is better, and the more rapid changing movements you make the more likely the tickrate is toc ause a problem, but I feel like almost everyone that posts about it is basically talking out of their ass. I'm not an expert by any stretch, hell someone that REALLY knows this stuff might come tear me apart, but I know enough to point out the stupidity of the picture. The reason you get shot behind a wall is because of latency tolerance and Blizzard programming the game to favor the shooter. When your client disagrees with the person shooting you, barring you using a survival ability which are coded to supercede this rule, or someone being too far outside of the grace period for latency tolerance, the server is going to favor the person taking the shot. This is because as much as it sucks to die or geet hooked around a corner slight, it sucks a lot more to KNOW you hit a shot and keep having the server say 'nah'.