The transaction was processed "under the radar," in order to hide it from the public, sources told public broadcaster KAN.
The Washington Post admitted it didn't give proper weight to Israel's denial of involvement in the shooting, which the Gaza Humanitarian Foundation has also denied.
IDF Spokesperson Effie Deffrin says aid distribution is undermining Hamas as the IDF presses ahead with expanded operations.
Moore was interviewed by The Jerusalem Post earlier in May, where he spoke about Evangelical Christians and support for Israel.
The military has allocated intelligence resources and reserve forces, and clarified open-fire orders for senior IDF commanders on the ground.
The military said it is aware of reports regarding casualties, and the details of the incident are being looked into.
Climate activist Greta Thunberg and Irish Game of Thrones actor Liam Cunningham are said to be among the Freedom Flotilla Coalition's crew voyaging to Gaza to deliver aid this weekend.