Nancy Friedman, on her blog, Fritinancy, quotes the OED on this usage: “one of many alleged group terms found in late Middle English glossarial sources, but not otherwise substantiated”.
Starlings are a pest species here in Melbourne, and to me the noise they make when settling for the night is more of a cacophany than a 'murmuration'. When they gather in nearby date palm trees around sunset, you can't hear yourself think. But maybe their flight involves a more pleasing and restful sound. After all, the Free Merriam Webster Dictionary defines murmuration this way:
: the act of murmuring : the utterance of low continuous sounds or complaining noises
murmuration of the crowds — A.E.Richardson> murmuration of prayer — Frederic Prokosch>
In case you don't want to follow those links, here is the Irish clip: