I'd rather not, I'm going out of my way to censor the name, so... Just in case, I don't want to initiate a witch hunt and instead talk to the admins directly if ever see that player on those servers again.

Some general info about the account if you care: Three years old, public profile, 1.5K hours in TF2, 100% achievements, about 10 Steam games with little play time.

100% achievements could hint at a cheating history but not necessarily. In the end none of this can be used to prove anything.

It's not a demo file, I was spectating them on the server. This is a recording of what I saw when I spectated them, recorded using Shadowplay.

I'm not sure if I should upload the entire video. Cutting out all the names will take a while. But many shots looked like that, just not all. I'm aware that cheats exist where you can toggle on and off and cheats that only activate if you aim within a certain vicinity.

I came across a Sniper on a server who headshot me in suspicious ways (instant headshot before I myself even turned a corner) so I went to spectate them, but they switched to Scout. I'm really not sure if they're cheating or not so I haven't yet reported them to the admins of that server.

Take a look at this: https://youtu.be/TRjBI4_bu-c

Not all shots are like that, so I'd guess it's a toggle or a vicinity thing. I'm pretty sure this kind of snapping onto the target by skipping pixels and skipping pixels right back doesn't happen with legit aim, but if anyone has more insight on that I'd love to hear it. Is this sufficient evidence of a cheat?

Also note that I always only saw that pixel skipping right when they took a shot. I can upload the entire video but I'd need to render it first and make sure I don't reveal any names so that could take a while.

Crosshair colors is stabbystabby's null-cancelling movement script coupled with a color changer script, which might also be by stabby but I'm not actually sure:

// Null-cancelling movement script
// (prevents you from pressing two opposing directions, which causes you to stop moving)

bind w +mfwd
bind s +mback
bind a +mleft
bind d +mright

alias +mfwd "-back;+forward;alias checkfwd +forward;dotxhaircolor"
alias +mback "-forward;+back;alias checkback +back;dotxhaircolor"
alias +mleft "-moveright;+moveleft;alias checkleft +moveleft;dotxhaircolor"
alias +mright "-moveleft;+moveright;alias checkright +moveright;dotxhaircolor"
alias -mfwd "-forward;checkback;alias checkfwd none;dotxhaircolor"
alias -mback "-back;checkfwd;alias checkback none;dotxhaircolor"
alias -mleft "-moveleft;checkright;alias checkleft none;dotxhaircolor"
alias -mright "-moveright;checkleft;alias checkright none;dotxhaircolor"
alias checkfwd none
alias checkback none
alias checkleft none
alias checkright none

// xhair COLOR toggle
//==========================================    ===============
alias dotxhaircolor "dotxhaircolorb"
alias dotxhaircolorb "cl_crosshair_blue 0; cl_crosshair_green 255; cl_crosshair_red 0;alias dotxhaircolor dotxhaircolorc"
alias dotxhaircolorc "cl_crosshair_blue 255; cl_crosshair_green 0; cl_crosshair_red 255;alias dotxhaircolor dotxhaircolord"
alias dotxhaircolord "cl_crosshair_blue 240; cl_crosshair_green 255; cl_crosshair_red 0;alias dotxhaircolor dotxhaircolorb"
//==========================================    ===============

Then, if you want the crosshair to turn black when you press Mouse1, you need to add this to your class config:

bind mouse1 "+attack; cl_crosshair_blue 0; cl_crosshair_red 0; cl_crosshair_green 0"

I'm not sure why but for me this breaks the ability to spectate the next player when I click Mouse1. If that also happens for you and you want to retain that functionality you need a script like this instead:

alias +blackCrosshairAttack "+attack; cl_crosshair_blue 0; cl_crosshair_red 0; cl_crosshair_green 0; spec_next"
alias -blackCrosshairAttack "-attack"
bind mouse1 +blackCrosshairAttack

This is my network config:

cl_cmdrate 66.67
cl_interp 0.0152
cl_interp_ratio 0
cl_lagcompensation 1
cl_pred_optimize 2
cl_smooth 0
cl_smoothtime 0.01
cl_updaterate 66
rate 10000000

You should probably record footage with "net_graph 4" so one can tell an unstable connection.

I'm aware this post is two years old and I'm terribly sorry for the necro, but time and time again I see people say that hitboxes in TF2 "lag behind" or point to other inaccuracies, and this is a thread that I've seen posted a few times as well.

What I want to make absolutely clear is that the OP's screenshots are virtually useless. They do not tell us when they actually took the shot. In TF2, the info that your target died/took damage doesn't reach your client until several ticks later (or frames in case of recorded footage), which can be more or less depending on your ping. This doesn't mean that your crosshair wasn't perfectly on point in the moment that you took the shot. In OP's case, their screenshots appear to be back to back, one frame to the next, so the first screenshot is without a doubt NOT the moment they actually shot.

On the contrary, the Soldier in those screenshots appears to have a blood decal on his face (it's already visibly poking out from below his cap on the first screenshot) which is likely to have been caused by OP's Sniper Rifle shot. Though of course that can't be proven.

I have a crosshair changer script that cycles between cyan, magenta and green on my crosshair whenever I press a movement key. Recently for my Sniper config I also bound mouse1 to +attack as well as turning my crosshair black, meaning my crosshair turns black on my screen the instant my game client registers my input. I've gone and recorded a lot of Sniper footage (under normal, non-laggy conditions) and have found that there was not a single time one of my shots hit while my crosshair wasn't on target (there were edge cases where the crosshair isn't quite on the head for a headshot, but you have to keep in mind that the head hitboxes are a lot larger than the visual model: https://i.ytimg.com/vi/WVvUwseSUXQ/maxresdefault.jpg). I have also not seen a single shot that was on-target and created a blood decal yet returned a miss from the server. TF2 by all means appears to have a very good netcode, which shouldn't be surprising given that it's the same engine as CS:GO.

I might make a video of all that footage in the future with an explanation of what's going on but for now, this clip demonstrates what I've been talking about:
https://youtu.be/AhQ4QE-01S4

For the record, when I play on a server with 40 ping, this is the order of events that ensue when I take a successful headshot (footage recorded at 60 fps):
First frame after taking the shot: The crosshair turns black, meaning my (local) game registered my input.
Second frame after taking the shot: Blood decal appears on the model.
Then, anywhere between the third and seventh frame (no idea why this is inconsistent but it's probably to do with server load when sending this info to each client, or my connection being unstable): On-hit particles spawn (CRITICAL HIT!!! message and blood particles), and shortly after that the damage number appears (either on the same frame or one frame later).

It's worth noting that until February 14 of 2017, there was a bug in TF2 that could cause hitboxes to be misaligned as demonstrated here:
https://youtu.be/tfl8TYQ1pbE
So any complaint/video footage made before that time could be perfectly valid in saying that there were issues with hitboxes.