Your latency and ping are unstable is all I'm driving at, even LTE is not designed for high stability (no satellite or cellular can be due to how it functions), so you doing "better" than them is subjective to how the lag comp is throttling their connection to the host to keep it more in line with yours. Their skill level also has nothing to do with their connection. Your connection is not more stable than theirs, the game's lag comp is just pulling them down closer to your own stability in order for you to have a gaming experience that's a bit more fair.
If there was no lag compensation, you would be that "easy target" to everyone with a broadband connection, the same with how it makes things more even for DSL users... without lag comp, broadband users would have an unfair advantage over everyone else.
As for server dedication, there is none - it's listen servers and peer 2 peer all around, which, as I just said, is exactly how you do better. Lag comp is on your side my friend... I'm sure you've had games where it just seemed everyone had the advantage against you as well, where lag comp was not in your favor - happens to everyone lol those games are more in line with where you'd actually stand with your connection compared to those of us with broadband. You might be a much better player skill wise, but when the connection isn't in your favor, or in the favor of player X with a stable broadband connection, you'd lose every gunfight simply due to the fact that you'd be out of sync with the host all the time..
A few friends of mine have "meh" connections and play very well when alone typically, but once they get into diverse groups of people with broadband connections, the lag comp favors the average in that connection quagmire, and suddenly they can't buy a kill...
Be mindful that your connection is causing others in the same match to lag which gives you opportunity over them.
Honestly, when you break down lag comp, it's sort of like a handicap for people like me >.< lmao I've played on a buddy's DSL before, swapping games back and forth on his account, and I do really well because it always seems like everyone is lagged behind me.. while playing at home here on broadband I have to try so much harder because I get throttled due to lag comp favoring someone like you, or him.. but I can't complain, makes it fair for him and you.. if it didn't, the CoD community would only consist of those with broadband connections.. that would be unfair for people that can't get said type of connection..