It's a "real number", a delta-v chart isn't really concerned with the realism of various missions. It's quite simply a table of velocity changes, how you would go about achieving these velocity changes is outside its scope.
As to how to calculate it, the parts of the journey in space can be calculated like any other part of the diagram, using the patched conic approximation to split it up into two body systems, and from then the Vis-viva equation (written on the chart).
The other lading/ascension values on the chart appears to consider atmospheric drag, but they skipped it for the Sun since any realistic drag model for a spacecraft there doesn't exist. It's just the speed you would crash into the Sun with from low orbit. (or more accurately, the way you have described it in your question, as a small elliptical transfer). Using the Vis-viva equation for the body you are currently orbiting isn't odd at all, it's the normal use case.
Are the relevant quantities for the Sun known well enough to give a reliable number? Yes and no. The Sun's mass is known very accurately due to accurate measurements of the planets orbiting it, but the other relevant number, the radius is more so-so. The Sun doesn't really have a solid surface, so the surface radius is more a question of definition than accuracy of measurements.
Lastly, it seems like a massive number, can it be right? Going from the surface of a body, and then navigating some in space, you would expect spending about the same delta-v as the escape velocity of the body. Given the Sun's escape velocity of 620km/s, this seems correct.