Of course people treat RSU grants as pay. It's taxed like pay and otherwise acts exactly like pay except that it's tied to the stock price. For many people it's the majority of the pay or an otherwise substantial component of the compensation structure.
I would certainly agree with you on the RSU front, although there is the other twist that some companies, like Google, don't equate RSU's 1:1 with actual shares, they can go up or down depending on other factors. So you can have 100 RSU's that convert to 1 share or 200 shares depending on how much your manager likes you. In that case it really doesn't matter if the stock price goes up or down.
To be fair it is a very creative way to avoiding the trap of over paying people. The bottom line is that all grants are legal contracts, generally very long and dense legal contracts, and it is useful to spend time to understand them. California is an "at will" state, if either you or the employer doesn't like the situation, either one of you can end it and be done.