Oktas,
That said, I have taught in the past that Va protects from full or abrupt control movements. At Va you may do full or you may do abrupt, but not both together. This is often overly conservative advice, but it takes into account the reality that Va is not a bullet-proof panacea.
I think that's how misconceptions about these sorts of things start! You should be teaching what Va actually is and not what you determine to be a conservative estimate of it. Testing (FAR 23.423) dictates a "sudden movement... to the maximum aft movement". The definition of Va and the requirements for testing at Va of control surfaces and their supporting structure hasn't changed since at least 1965. There have only been slight wording changes. You can look that up under the historical FARs.
Va is bullet-proof for what it is. It gets the misconception that it isn't bullet-proof when people break airplanes while flying at or below Va but the problem isn't Va, the problem is the pilot's understanding of Va. Example: AA 587.
Most American Airlines pilots believed that the tail fin could withstand any rudder movement at maneuvering speed.