Originally the word "hacker" made no distinction between the two meanings. This site is pretty old, so you're right, it was intended in the original "Kevin Mitnik" sense (the original hacker, who ironically would fall outside of the modern definition)
The modern acception focused on online computer security came much later. That meaning is neither the one used in the name of this site nor the one that would be relevant to this conversation.
To summarize: today's hackers are also yesterday's hackers, but yesterday's hackers may or may not be modern hackers.
> In the sense of the word that means people who write code, not people who break into things
It would be like if you were going over a list of pros and cons and when you got to the cons some guy was like "wow, you work with criminals, huh?" Then you tell him not that sort of con and he says "yeah, typical nerd bickering".