Weird Thought: Could the Pentagon have been Hit by a Cruise Missile fired by the Russians as Part of their Military Exercise on 9/11?

From Paul Thompson's Timeline.

The 9/11 Commission later concludes that had Flight 93 not crashed, it would probably reach Washington around this time. The commission notes that there are only three fighters over Washington at this time, all from Langley, Virginia. But the pilots of these fighters were never briefed about why they were scrambled. As the lead pilot explained, “I reverted to the Russian threat … I'm thinking cruise missile threat from the sea. You know you look down and see the Pentagon burning and I thought the bastards snuck one by us …. [Y]ou couldn't see any airplanes, and no one told us anything.”

Could the Pentagon have been Hit by a Cruise Missile fired by the Russians as Part of their Military Exercise on 9/11?

I really have no idea how likely this idea is, but it might explain the extreme cooperativity between the US and Russia since 9/11.

This theory certainly does provide a more plausible explanation for how a cruise missile could have hit the Pentagon than the idea that a US missile was launched to target the Pentagon.