Different sources trace back to the Greek grammarian Aelius Herodianus (2th century AD), the author of a most unusual compendium of exceptions Περὶ μονήρους λέξεως; see the following passage from A Companion to the Ancient Greek Language (ed. Bakker, 2010):
Montanari's Dictionary of Ancient Greek (Brill) lists four words that start with the spiritus lenis:
with the following note, "initial smooth breathing by dissimilation, cf. Hdn. 1.546.21, 2.940.16 in mss. and edd. Ῥα- can also be found, prob. by analogy."
I also searched the Loeb and it seems it could be simply an editorial choice:
cf. ᾿Ρᾶρον (Pausanius) or ᾿Ρα[ριά]δος (Select Papyri) vs. τὸ Ῥάριον (Pausanius, mentioned in Montanari as "simpl. τὸ ᾽Ράριον" - note the difference) or Ῥάριον (Hermesianax).
Goldstein 2013 writes that “The rhotic /r/ was probably an alveolar trill (Allen 1987:41). According to ancient grammarians ([Arc.] 226.24-227.2 Schmidt 1860), it had aspirated and unaspirated allophones, which were subject to the following distribution: word-initially it is aspirated, e.g. rhanis ‘drop’; when geminated word-internally, the first segment is unaspirated, the second aspirated; otherwise, /r/ is unaspirated. Evidence for this distributional pattern comes from inscriptions and Latin orthography. For the first, Phrearrios is written phrearhios and phrearrihios on the Themistocles ostraka of the 480s BCE. For the second, Latin rhetor, Tyrrheni, and Socrates illustrate all three patterns.” (Goldstein 2013)
Leslie Threatte (Threatte 1980, volume 1) writes that “the ancient grammarians prescribe that initial rho and the second of two intervocalic rhos be aspirated.” She mentions some interesting epigraphic data, e.g.
[— — — Φρ]εάρℎιο[ς] (IG I³ 723; ca. 500 BC)
ῥοϝαῖσι (IG IX1 868.3).
Kavitskaya 2002 claims, citing Wetzels 1986 (p. 315), that “There is evidence that aspirated rho (>*sr) was originally realized as a voiceless r” (p. 72). It seems Wetzels’ claim is partly based on Harviainen 1976.
cf. Dorandi 2006 "More complex is the situation concerning aspiration and accents which are both marked only rarely and then often arbitrarily. The spiritus lenis (smooth breathing) is marked less often than the spiritus asper (rough breathing)"
Lundquist 2013 reminds that
"These symbols [the spiritus asper and the spiritus lenis - Alex B.] were not in the autographs of authors writing prior to this convention, and texts so printed reflect Alexandrian editorial work. Concerning aspiration in the literary corpora, we should note that although our Ionic literary corpus is generally transmitted with aspiration on the model of Athenian texts (while Lesbian remains psilotic), this may in many cases be merely conventional."
He mentions an interesting example:
"all MSS of Semonides of Amorgos’ ‘On Women’ 82 give khōs, crasis of the particle ke and hōs, but a recent editor, Martin West ( West 1989), prints instead kōs to better represent Semonides’ East Ionic ōs.
Thus, he concludes by saying
"Whether we should print aspiration in Ionic authors remains in a number of cases disputed; as becomes clear from the evidence discussed above, our most reliable sources for psilosis are epigraphic."