Is this accurate?

It appears to be quite the opposite, actually. Without even looking at the role of music in the Church, folk music was an important cultural facet of the Medieval period and one that is surprisingly well attested in Early Medieval England, considering that no actual examples of the music itself survive.

Sources like Beowulf - in which the feasts at Hrođgar's hall are always accompanied by ælu-scops playing the harp and regailing the assembled warriors with poems and songs of great deeds - attest to the centrality of music and poetry to Early Medieval English feasting - and indeed Beowulf was likely performed aloud at feasts accompanied by harp or Saxon Lyre - but this was far from just an elite affair.

Bede dedicates part of his Historia Ecclesiastica to telling the story of Cædmon, the earliest named English poet, who, according to Bede at least, was blessed by God in a dream with marvellous songwriting ability ((British Library, Cotton MS Tiberius A XIV, f. 1r). According to Bede, before his revelation, Cædmon was a simple cowherd who worked as a hired labourer at Whitby Abbey. Cædmon's revelation comes while he is sneaking off to the Abbey's stables, which he did "as soon as he saw the harp approaching him" as he was embarrassed by his singing voice. Bede's implication is that communal singing backed by a harp or a lyre was a commonplace acitivity for day labourers, either actually during the course of their work or as a means of relaxing at the end of the day. Indeed, Bede recounts that the workers would pass a harp or Saxon Lyre around and take turns leading and playing songs to each other (as opposed to a single performer entertaining everyone), which suggests that at least some level of basic musicality was commonplace among the general population