this 'information' comes from Nennius where I think he has builc tho in the modern translation - see http://www.fordham.edu/halsall/basis/nennius-full.html - the name is rendered 'build' - I suspect builc went to buile (easy misreading c for e) and then to binle (u and n are virtually indistinguishable in early handwriting) then by usual rules to Binley - there is a brief discussion in one of the footnotes to Chaloner by J G Cumming which I think makes the same point.