What's sad about this interaction is that, at least for me, if that person had said "Hey, we actually already hired somebody for this, but I'd still love to meet up for lunch and hear how you'd approach some of these problems" I'd do it.

I like problems, and I like solving problems. I've been lucky enough that the pay is honestly just a bonus most of the time. Having a contact at a company I think is cool is way more valuable to me than the cost of taking a train an a few hours of my time.