He wrote the story with his friend's 'assistance'. = He wrote the story 'with the assistance of' his friend. [=his friend helped him to write the story]
Our family had to 'go on public assistance' [=receive money from the government] when my parents lost their jobs.
Nobody 'came to her assistance' [=nobody helped her] when her car broke down.
(..) But by the same token I also smuggled my share of weapons in exchange for those illegal substances, with the full knowledge and assistance of both the DEA and CIA. Betzner says that in he flew weapons from Florida to El Salvador, and drugs from Colombia to the Bahamas on the way back. (..)2009 Loose Change 9/11: An American Coup