It DOES happen all the time. A company offers a job, the candidate makes a counter-proposal for a bit more money [or additional vacation time, or a deferred starting time, or a bigger bonus, or additional tuition assistance, or any other benefit the candidate asks for from the company].
Why would the candidate risk losing credibility? It is different making those requests PRIOR to an agreement being formalized and agreed upon, versus when it is being negotiated.
Are there instances where the candidate just takes the first offer? Sure -- but it is ABSOLUTELY common for the candidate to negotiate.
If a contract is in place, that is different. But while it is being agreed to? That's called negotiation.
And jsshap, I know you are a lawyer, so if it came off above as me questioning your knowlege of contracts, that was not intended.