Yes, a two-way relationship, but that doesn't mean you have equal leverage. They have way more leverage, especially if they are a good company and pay well.
I think I confused "two-way street" to mean an equal-sided transaction.
You leverage depends on your position and is not clear cut.
If you are interviewing to have an alternative to another offer, you might effectively dictate the process (time spent, deadlines etc.) if they want to interview you bad enough. And I’ve been on the receiving end as the recruiting company’s interviewer, pitching the job to get a favorable answer.
Same if you don’t have any pressure to leave your current job.
Sure big companies sometimes won’t have any leeway to deal with these candidates, that’s also why they get avoided by people who have the choice, and everyone’s happy.
I think I confused "two-way street" to mean an equal-sided transaction.