Can we please talk about the huge conflict of interest with the Surgeon that removed the tumor….DOING THE FRIGGIN AUTOPSY!
Malpractice lawsuit!
While this is VERY technically possible, it wouldn't fly for a variety of reasons.
1) Medical examiners are government employees (usually at the city/county level), NOT hospital employees.
2) The medical examiner's office is NOT in the hospital. Cities that have their own have a separate location for them, and smaller cities/towns usually share a county facility.
3) As you point out, the conflict of interest is huge, and double-sided, as neither the hospital nor the government are going to want a blatant appearance of impropriety*. This is especially true on the government side, since in a lawsuit any competent attorney (and most incompetent ones) would make mince meat of the same person who performed the surgery performing the autopsy.
Could it technically happen? Yes, in that there technically aren't laws against it. But it would require a government employee moonlighting as a surgeon, both the hospital and the government not caring (including no rules in their job description about additional work that conflicts, which is normal language for government employees), and no one worried at all about the conflict of interest.
*This happening would almost certainly involve a high level of corruption/conspiracy, which admittedly is appropriate for Sunnydale. If it WAS going to happen, Sunnydale is actually a likely location, since we know that there are those in the know who actively things up anyway.