When the company is the first to give a number, you always get the job, and you have a 50% chance of getting a high salary.

No... Let's say you're going to the store to get milk. Either milk will be on sale or milk will not be on sale. We've covered the universe with our proposition. Nevertheless, the presence of two options is irrelevant to their respective probabilities. Assigning a uniform prior to the options is downright absurd.

I believe what he means to say is this:

    No employer is going to lower their offer because you've asked for more.