I think Wikipedia is using "Vedic scripture" as a metonymy for Hindu scripture in general. It is the Puranas which have statements that seem, at least on the surface, to indicate that the Moon is farther from the Earth than the Sun. Here is what this chapter of the Vishnu Purana says:
The sphere of the earth (or Bhúr-loka), comprehending its oceans, mountains, and rivers, extends as far as it is illuminated by the rays of the sun and moon; and to the same extent, both in diameter and circumference, the sphere of the sky (Bhuvar-loka) spreads above it (as far upwards as to the planetary sphere, or Swar-loka). The solar orb is situated a hundred thousand leagues from the earth; and that of the moon an equal distance from the sun. At the same interval above the moon occurs the orbit of all the lunar constellations. The planet Budha (Mercury) is two hundred thousand leagues above the lunar mansions. Śukra (Venus) is at the same distance from Mercury. Angáraka (Mars) is as far above Venus; and the priest of the gods (Vrihaspati, or Jupiter) as far from Mars: whilst Saturn (Sani) is two hundred and fifty thousand leagues beyond Jupiter. The sphere of the seven Rishis (Ursa Major) is a hundred thousand leagues above Saturn; and at a similar height above the seven Rishis is Dhruva (the pole-star), the pivot or axis of the whole planetary circle.
And here is this chapter of the Srimad Bhagavatam says:
Thus the time the sun takes to rotate through half of outer space is called an ayana, or its period of movement [in the north or in the south]. The sun-god has three speeds — slow, fast and moderate. The time he takes to travel entirely around the spheres of heaven, earth and space at these three speeds is referred to, by learned scholars, by the five names Saṁvatsara, Parivatsara, Iḍāvatsara, Anuvatsara and Vatsara. Above the rays of the sunshine by a distance of 100,000 yojanas [800,000 miles] is the moon, which travels at a speed faster than that of the sun. In two lunar fortnights the moon travels through the equivalent of a saṁvatsara of the sun, in two and a quarter days it passes through a month of the sun, and in one day it passes through a fortnight of the sun.
But many people interpret these statements differently. See, e.g. Richard Thompson's book "Vedic Cosmography and Astronomy", which interprets these statement as referring to heights above the orbital plane as opposed to actual distances from the Earth.