It's a mere saying tbh. It was just a coincidence imo that Bitcoin was born after the recession of 2008. That, or Satoshi intentionally did it to create more impact when Bitcoin is released. Still, it isn't entirely related though, since Satoshi never aimed to stop recession with Bitcoin, it was never his goal. The goal was to simply create another system of transaction without a need for a third party to manage it.

The Bitcoin mirroring stocks part isn't really that legit, cause if so, then what happened right now? Bitcoin has well above recovered, and yet stocks are still having difficulties. The damages of the pandemic last March was the cause as to why both stocks and crypto went down badly, but it isn't enough to become the basis that stocks and Bitcoin price are connected to each other.