After going through all the steps with a big corp, I was "offered" to do an additional interview if I wanted to be assessed at my current level (they leveled me lower). I stood my ground and respectfully declined, and eventually they made me an offer for the correct level. What I learned the hard way was that you need at least one more competing offer, otherwise you won't have any leverage.
Resembles a date. Dating and interviewing has much in common. Judge a person in the time it takes to drink two beers to see if you want to stick together. It's all hunches and feeling and there is no need to over analyze it.