If you paint a copy of Mona Lisa, it will be under your copyright, because of the provenance. There will be no doubt that it's your work, not Leonardo's.
That’s actually incorrect. In your example it’s fine only because the painting is old enough to be in the public domain. In general (with rare exceptions) you can’t paint an exact copy of a work under copyright and then utilize that copyright without permission of the original copyright holder. What you’ve created is a “derivative work.”
If you paint a copy of Mona Lisa, it will be under your copyright, because of the provenance. There will be no doubt that it's your work, not Leonardo's.