There is no such thing as “directly” DX. The drivers of the major GPU vendors on Windows must also implement DX ontop of their internal abstractions over the hardware.
While Vulkan will theoretically always have more “overhead” compared to using the hardware directly in the best possible manner, the latter isn’t even close to being done anywhere as it’s not feasible.
Therefore, situations where a driver implemented atop of VK being faster than a “native” driver are absolutely possible, though not yet common. Other real-world scenarios include Mesa’s Zink atop of AMD’s Windows VK driver being much better than AMD’s “native” OpenGL driver, leading to a dev studio of an aircraft sim shipping it in a real game.