Halliday & Matthiessen (2004: 473n):
Strictly speaking the embedded ‘fact’ clause functions as Head of a nominal group which in turn functions as an element in the ranking clause. This analysis shows how clauses serving as Head are agnate with clauses serving as Postmodifier in nominal groups with a fact noun as Head: that Cæsar was ambitious is obvious : the fact that Cæsar was ambitious is obvious. But since a fact clause functioning as Head takes up the whole nominal group we can just as well leave out that stage in the structural analysis and show it as directly embedded into the clause …