Keep in mind they can and will still low ball you on salary and expect you to negotiate, though they have a ceiling on the salary for psychiatrists. I negotiated about a $30k annual increase from the initial offer I received, matching what another hospital in town was offering me.
You can negotiate work hours, flex time, number of patients per day, bonus amount, responsibilities, amount of call if any. Source: I did and still do periodically.
Different departments will negotiate differently based on who is in HR and who is chief of the department, who is director, how bad they want a psychiatrist, etc. The VA is not as monolithic as it seems. If a VA location is going to be rigid and married to a job announcement no matter what, I would walk. If they really want you they'll find a way to make it work within reason.