As with most things, it's hard to prove what actually happened definitively, but there are clues you can piece together to make a claim within a reasonable degree of probability. Things like what type of binaries were installed, what servers were reached out to, even what commands were run...if you collect enough data, it is possible to see patterns in how certain attackers (like USCC) operate, and if we assume a teenager in her parents' basement doesn't have access to the same tools and procedures as USCC does, then it becomes pretty obvious it wasn't her.
To a certain degree, if your server has malware X, and you can identify malware X (or something very similar) as belonging to actor A, and you know actors B, C, and D don't have X in their arsenal, then you can guess with high probability that you were attacked by A.
Intelligence is probably the most high stakes guessing game in history, and there are definitely smart people at the top who know that simple IP correlation is not enough to make this claim - but they likely have access to sensitive (confidential) data that further justifies that claim.