Has Churchill said something like this?
Ori, this is right on the cusp of being idiomatic. I hope that my explanation will help you better understand the present perfect [PP].
Yes, we use the PP for finished events but that's when those finished events have a relevance to now. As you already know, the PP has a strong connection to 'now'.
But I feel, and I'm certainly willing to hear other viewpoints, that this example is not the PP of current relevance/importance, rather, your example could be glossed as a PP of experience, in that you are asking if Churchill ever had the experience of saying such and such.
But because Churchill is dead, [this in itself doesn't preclude the PP] and more importantly, long dead, the tendency, I think, would be to use the simple past,
Did Churchill [ever] say something like this?
To me the connection to 'now' is sufficiently disconnected that I doubt you'd see the PP being used in this case.
The past perfect [PsP] wouldn't work here unless you were trying to point to a what he said in connection to another event at a different point in time.