Learn English – Miss/Break A Curfew

"From" is referring to the "report" (not to "published").

Here's the same text rearranged and simplfied:

A report from Angus Armstrong and Monique Ebell of the National Institute of Economic and Social Research, a private think tank, was published Tuesday. It estimates [...]

Typically investigation is followed by of or less commonly into. On is used even less often, though I have seen it before. I think that the headline would read more naturally with "Investigation Of Accuracy Of CNN" or better, to avoid the double "of", as you suggest, "Investigation Into Accuracy Of CNN."

A Google ngram of the three phrases shows "of" being used roughly ten times more than "into," which is used roughly five times more than "on."

As with any words or phrases, these three phrases aren't exactly identical, but I can't find any hard and fast rule for their usage. The only one that I was able to think of is that when criminal investigations are being discussed, "investigation into" is typically used.

The police have started an investigation into the murder of John Smith.