I'll respond to the last question: yes. I might lie, but I'll answer.

In fact, I was at Ikea the other day and a rando asked where I worked, so I told them about the business, but my the name of the company. It turns out they studied something relevant, so we had an interesting conversation.

The company I work for is big enough they wouldn't be able to dox me or anything, but it is something I'm willing to discuss.

As to the first, I also saw it as 100% a joke, just like the OP. It's just a funny thought, that's all.