In this case, the person renting the car would be "interviewing" the car rental company to determine if their service is worth their money.
It goes both ways... the rental car agency interviews the person to make sure she is trustworthy of driving the car. The author is asking you to think about the relationship a little more abstractly than simply who is giving money to whom.
Having said, that, I think this is a poor analogy because I don't find it particularly illuminating and the situations just don't seem very... analogous.
If Carpenters Were Hired Like Programmers
Instead of "whoever is giving up money should do the due diligence," I would suggest you consider "both sides should do increasing due diligence as the importance of a decision increases."
From this perspective, the article is pointing out the dumbness of some due diligence methods currently being used at software companies.
To walk into a job interview with the same expectation of being "served" is ridiculous. It's true that if they're smart, they will try to entice you and provide a nice experience, but primarily they are trying to decide whether to spend large amounts of time and money on you versus someone else. Most companies are not in the business of quickly and efficiently hiring as many people off the street as possible. You can be flustered by an interviewer's poor technique, but don't be impatient to receive the job offer you feel entitled to.