I somewhat disagree with this opinion
As you further note in your post, the main difference lies in the volatility part. Any you are right since it is the exact reason why you think there's no correlation between Bitcoin and the stock market. Simply put, Bitcoin's volatility is hiding this correlation, but you can be damn sure it is still there (only gold and other precious metals are negatively correlated to regular stocks in a genuine way)
Bitcoin is a highly speculative asset, and it is the same speculative money that gets poured into stocks and cryptocurrencies alike (with more emphasis on the speculative part in case of crypto). So, as far as major trends and market shifts are concerned (think financial crisis here), I for one expect Bitcoin as well as other cryptocurrencies to behave in a pretty predictable way (read, they will crash along with the stock market)