The name is not incidental. According to local tradition, the well earned it by moving, of its own accord, from one side of the road to the other, in apparent protest at a desecration.

The story, recorded by pupils at Ballybunion School and preserved in the Irish Folklore Commission's Schools' Collection, holds that around a century before the account was written, a woman washed clothes in the well on a Saturday night, profaning it. When Sunday morning came, the well had relocated itself to the opposite side of the road or pathway. After that, the pattern of devotional practice known as "rounds", the ritual circuit walked around a holy well while praying, ceased entirely. The school folklore notes that if the well truly moved, then the rounds had previously been paid in front of it rather than around it, since circling the original site would have traced a slightly longer but nearly identical path. By the time the folklorist Caoimhín Ó Danachair visited and recorded the site in 1958, the well was no longer being visited as a holy place, though it was still remembered as one. Two legends clung to it: that a sacred trout lived in the water, a common feature of Irish holy wells where a fish was thought to embody or guard the well's sanctity, and that the well had made its famous crossing of the road. The well also appears, marked as Toberreendoney, on Ordnance Survey maps from 1840 to 41 and again in 1915, confirming it was a recognised feature of the landscape across that period.

Today, very little remains. The County Council closed the well, and what survives is a trickle of water at the roadside near Doon Glenn, at the foot of a cliff roughly a hundred yards from the shore. The schoolchildren who recorded its folklore noted that the water was always almost ice cold, and that there was no bush of any kind near it, an absence that itself stands out, since holy wells in Ireland are frequently marked by a thorn or elder hung with votive offerings. This one has none of that. Just cold water, a road, and a name that remembers a Sunday morning when something, supposedly, shifted.