This has never been the case, and it's very much not the case now given the market.
From running Taro, these are ballpark numbers I've see on conversion numbers:
On a final note, referrals will have far more weight in startups compared to Big Tech as startups are more tightly knit.
Nope. Remember, not all referrals are created equal.
If the person referring you is a Director+ at the company saying "this is the best person I've ever worked with", then an interview is guaranteed. Short of that, I would not assume it's guaranteed.