This rule is implied by the Comparative Tables, where medial aspirates became voiced spirants (PE19/23). Since at first aspirates became voiceless spirants, this means those medial voiceless spirant must later have become voiced. The examples in The Etymologies indicate this change occurred medially after vowels (Dor. hedhu), but not after consonants (Ilk. Balthor) or finally (Ilk. tâch).

In the Comparative Tables, the medial development for the aspirate [kʰ] is somewhat obscure, given as “kh > h > -” (PE19/23). Since medial [h] did not disappear when it developed from khw, I think the likeliest explanation is that the velar [x] that developed from [kʰ] first voiced to [ɣ], after which the [ɣ] vanished.

There are numerous examples of final unvoiced spirants in Ilkorin, such as breth < ᴹ✶b’rethā. This implies that the medial voicing occurred after primitive final vowels vanished. It cannot be the case that final spirants later lost their voicing, since there are also examples of final voiced spirants, such as gwedh < ᴹ✶wedā.

There are a number of names that are possible counter-examples to this rule: Ilk. Brithon, Dor. Lúthien, Dor. Thuringwethil and Ilk. Denithor. Most of these can be explained as later compounds, but the last is given an explicit primitive form ᴹ✶Ndanithārō [ndanitʰārō] and cognates in other languages (LR/188). This name does not appear in The Etymologies, so perhaps Tolkien was thinking of another phonetic scenario when this name was coined.

Helge Fauskanger (writing before the Comparative Tables were published) suggested an alternate theory: that the medial voicing did not occur between vowels, but only before certain consonants (AL-Doriathrin/hedhu). The two clear examples of this change showed this development only before [w] and [m], so perhaps in between writing the Comparative Tables and The Etymologies, Tolkien decided that the medial voicing only occurred before labials or some similar scenario.