It was my mistake, I said that we definitely know they don't vs. there is no evidence showing that there is. There aren't much studies to back this up. The whole point of the talk is that software engineering as a discipline is really poorly studied and we tend to make assertions like this without actually validating them.
If I was betting money on this(I.e. deciding where to focus my investment), the quality of the typesystem would only matter if the typesystem caught real problems that I face in my day to day work. For a Web app for instance, it makes no sense to use Rust vs a GC'd language because the kinds of bugs that you face in Web apps aren't really the kinds of issues that a borrow checker will help you with. The whole point of Rust being difficult is that it saves you time down the line, if it's difficult and it doesn't then that tradeoff doesn't make sense.
Hilel teaches formal verification for a living, he very much sees the value of automatically proving properties about your program, as do I, but the reality is that the typesystem doesn't necessarily help as much as we think it does.