In fact, this distance and size does not check out with the radiation spectrum the sun emits (it suggests a certain minimal temperature, which we'd probably feel a lot more then we do if it was this near), and by checking visually (just looking at the sun with dark sunglasses) one can only figure out the apparent size, which is just the relation between the distance and the diameter of the sun, not actually a numerical value for one or the other.

So, yes, the figures in the wiki are very, very strange speculation and are basically the same as saying "I think I have reason to believe that the figures found on wikipedia don't represent reality, but I do not have any idea what they should be instead."

However, one could try to triangulate the sun's distance by having two people at a southern and a northern location face in the same direction and write down the sun's apparent location relative to their field of view, for example relative to the center of their vision. Then, you actually have the data to "draw" a triangle with the two people's distance as a base that has two lines attached with an angle corresponding to the position in the two people's field of view. If you have that, you can measure how far away the pointy end of the triangle aka the sun actually is.

If you do that, you'll most likely find out that the sun is so far away that you have problems getting a reliable distance because your measuring errors will matter too much. With that said, figuring that out will still give you a minimal distance. So, for example, you'll find that the sun is somewhere between infinitely far away (= you go two times the exact same angle) and only very far away (= you take one time the angle you got minus your estimated measuring error and one time the angle plus you got plus your estimated measuring error).

If you get some extra equipment to refine that you'll actually be able to confirm the wikis data if it is correct (against the odds) or get the lower end of your results range (which depends on your measuring error) high enough to proof that the wikis distance is too low.