Just why would we ever assume there was no video?
Are not all fighter/attack aircraft equipped with recording devices?
Would it be unreasonable to assume after such an event as this, the video would be pulled and retained for use in any inquiry?
As to whether someone "lied"....I would have to be convinced they did so with intent to deceive and did so knowingly. I also consider a willful omission of a fact to be equal to lying.