It all makes sense when you realize that they're lying and their "automated system" is a bunch of low level contractors.
If you have worked in any company that deals with internet-facing traffic serving the size of audience that Twitter does, it should be obvious that 1k employees is nothing if you want to have all the necessary teams you need to keep the business running, for example, software engineering, software support, hardware engineering, hardware support, network engineering, software engineering, HR, finance, legal, PR, management, IT department, etc.
A company of this scale is not just code and raw technical skills. There are many nuances that you need to appreciate before you understand why it involves 1k-5k employees.
Typically it doesn't happen because it's more profitable to use data scientists to sell more ads.
I've reported someone leaking Polish court documents of an ongoing case on Facebook - nothing happened.
I've reported a YouTube video praising Anders Breivik as an European hero defending whites from Marxists, Leftists and Muslims - it's still up.
I've created a Twitter account and it got instantly locked for being 'suspicious' or 'automated' (but of course giving them my phone number would fix it instantly) - https://news.ycombinator.com/item?id=17014511
What are the nuances that I'm missing?
I challenge you try and think through why your simple spam filter and human appeals process will not scale to Twitter's size. What kind of throughput can it handle? What happens when there is more content being appealed than the review team can handle? How do you prevent attackers from maliciously flagging other users' content? How do you handle advanced threats where attackers compromise existing accounts then begin to spam, thus bypassing any "easy" checks like looking at account age? How do you classify "hateful" speech? How does it scale to foreign languages, slang, etc?