At that point, you could say "I'll give up all my equity for another $100", at which point the boss would jump to agree.
Not because $100 is too much, but because you've annoyed her by asking too many times. $100 is still trivial in value to the business.
The point was just a thought experiment to show that equity has more than 0 value.
OK, equity is worth five cents an hour. I admit it! Let's all negotiate with that in mind.
It's quite something that you apparently couldn't tell the difference between those two things.
If I offer my Embarcadero penthouse in exchange for a $100/year raise, does that mean the apartment has 0 value?
The article clearly wanted you to ask for a raise at at least the granularity of real negotiations. Try getting a $10K raise in exchange for giving up equity.
This will be possible (for people operating in the eng compensation band) at almost any startup you might want to work for. If you ask for this, and they don't at least discuss it with you, it's a pretty strong sign that you don't want to work there.
You don't generally want to work somewhere the company leadership doesn't value the future of the company.
If you can get a $100/year raise just for the asking, and you can also get a $100/year raise in exchange for equity, then simple arithmetic indicates that the equity has zero value.