I think the two meanings of "oversight" are not quite interchangeable. One is a mass noun (used without an article): "better oversight is needed"; while the other is a count noun (used with an article): "it was an oversight". So "because of oversight" sounds odd to me; I think it would be "because of an oversight", which would unambiguously indicate the "error" sense.

"The activity was sanctioned because of the oversight" seems to work for me with both meanings of 'oversight'

Ah, very good.