GitHub is connected, not typed: you sign in with GitHub and we read the account you signed in as. That is why it carries a tick, and why nobody can claim someone else's.
LeetCode and Codeforces are plain usernames, and we check the username exists on that site before saving it. They are not proof of anything, and they are not shown with a tick.
Stats
Public stats from those sites are fetched and cached. If a number is behind, it will catch up; if a profile is private there, nothing is shown.