'Oversight' is a most ambiguous word. To be given 'oversight' of something is to be given the task of supervising it, inspecting it or managing it. You sometimes see the word used this way in job descriptions and advertisements. It was the original sense, dating back to the early 15th century.
The noun came from the verb 'to oversee', which goes right back to Anglo-Saxon times, although then it meant literally to look down upon something from above, with your eyes rather than your mental faculties.
'Oversight', though, has another important meaning. It also means passing over something without seeing or noticing it: being negligent, in other words. Or you might be able to point out 'an oversight': a mistake.
This meaning arrived slightly later, appearing only at the end of the 15th century. The two meanings, positive and negative, are used today in about equal proportions, which is a recipe for confusion.
What's wrong with 'supervision'?