This is almost definitely "Noise Level" (1952) by Raymond F. Jones.
The only difference is that instead of telling the scientists that the Soviets had developed working anti-gravity, the project leader showed the assembled scientists a (faked) movie showing the anti-gravity device in operation, and claimed that the government had lost his notes.
The scientists do ultimately succeed in developing anti-gravity, though they initially think their efforts are a failure because their machine is much bulkier and uses a lot more power than the one they were shown.