Black hat knowledge for white hat programmers
I'm coming in late on this, as I just heard about it on the podcast. However, I'll offer my opinion as someone who has worked on the security team of a software company.
We actually took developer education very seriously, and we'd give as many teams of developers as possible basic training in secure development. Thinking about security really does require a shift in thinking from normal development, so we'd try to get developers thinking in a how-to-break-things frame of mind. One prop we used was one of those home safes with the digital keypad. We'd let developers examine it inside and out to try to come up with a way of breaking in to it. (The solution was to put pressure on the handle while giving the safe a sharp bash on the top, which would cause the bolt to bounce on its spring in the solenoid.) While we wouldn't give them specific black-hat techniques, we'd talk about the implementation errors that cause those vulnerabilities -- especially things they might not have encountered before, like integer overflows or compilers optimising out function calls (like memset to clear passwords). We published a monthly security newsletter internally, which invited developers to spot security-related bugs in small code samples, which certainly showed how much they would miss.
We also tried to follow Microsoft's Security Development Lifecycle, which would involve getting developers to talk about the architecture of their products and figure out the assets and possible ways to attack those assets.
As for the security team, who were mostly former developers, understanding the black-hat techniques was very important to us. One of the things we were responsible for was receiving security alerts from third parties, and knowing how difficult it would be for a black hat to exploit some weakness was an important part of the triage and investigation processes. And yes, on occasion that has involved me stepping through a debugger to calculate memory offsets of vulnerable routines and patching binary executables.
The real problem, though, is that a lot of this was beyond developers' abilities. Any reasonably sized company is going to have many developers who are good enough at writing code, but just do not have the security mindset. So my answer to your question is this: expecting all developers to have black-hat knowledge would be an unwelcome and detrimental burden, but somebody in your company should have that knowledge, whether it be a security audit and response team, or just senior developers.
At the end of the day nothing the 'black hats' know is criminal knowledge, it's just how the knowledge is applied. Having a deep understanding of any technology is valuable as a programmer, it's how we get the best out of the system. It's possible to get by these days without knowing the depths as we've more and more frameworks, libraries and components that have been written using such knowledge to save you having to know everything but it's still good to dig from time to time.