The Lord Chancellor and the Lord Chief Justice had indicated their intention to remove Dr Andrew Reid from judicial office following the investigation.
But despite being entitled to challenge their decision, the senior coroner decided to stand down.
During her time as deputy assistant coroner, Ms Greenaway conducted 12 inquests in Camden, but worked largely from Poplar Coroner's Court in east London.
According to British law, Ms Greenaway, who also worked as a nurse in Australia, would have needed either five years with the Law Society or five years of experience as a qualified medical practitioner.
She met neither set criteria.
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The 78-year-old woman suffered serious injuries after her bag became trapped between the doors of a train at Notting Hill Gate station.
The oil has affected wildlife and boat owners have been told not to move their vessels to avoid spreading it.
Fearing for public safety, PC Chegwin pushed her in the chest in a defensive manner, not knowing she had extensive breast surgery.