Are you saying $20 for a burger and drink is trivial unless one is "dirt poor"? That doesn't match my estimates of the distribution of wealth in the US, and certainly not the world.
I don't think a $20 burger and drink is a simple, common social expense for everyone. Certainly not on a frequent basis.
If you're curious how I handle those friendships: I invite them to dinner at my house. Much as discussed in the article.
If most people eat lunch out once a week for $20 - that's about $1000/yr. That's trivial for most people if it's part of their social/entertainment expenses (eg even making $30-40k), but it's okay that it might not be trivial for all people.
Obviously trivial expenses are the first to be optimized away when a budget crunch occurs, because they are also trivial to remove/stop. It's hard to delay rent or a car payment withour real consequences, but there's no real consequence to not eating out lunch anymore.
I mean if you are stubborn enough you'd find anything innocent to be malicious but I'd wager most people would think nothing of it unless you do it every single time and also refuse reciprocal offers
People without disposable income tend to do this naturally. Hanging out doesn't have to mean always going somewhere and buying stuff at a large markup. You can have as much or more fun hanging out at someone's house/apartment, a park, the beach, going for a hike, etc.
What kinds of things are you paying for, though? Consider there's a subtle, unintentional message if you insist on paying for their $20 burger and drink: "This $20 is a big deal to you, but not to me." Unless they are dirt poor, they can probably pay for themselves for most things.
Myself, I have friends with 10x less money (self-employed), and 10x more money (huge stock options and the company popped) -- in both cases, we round-robin the check at dinner. Now mind you, we're not going to French Laundry...