Halliday & Matthiessen (2014: 537-8):
The ‘fact’ noun serving as Head/Thing of the nominal group may thus embody a form of assessment of the projected clauses serving as Postmodifier/Qualifier – assessment involving modalisation. Premodifiers may provide further assessments of the projected clause, either as attitudinal Epithet (e.g. painful, interesting, obvious; cf. good in good chance above) or as post-Deictic (e.g. alleged), e.g.
‘The U.S. government has to come to terms with the painful fact [[that the good old days [[when it could just borrow its way out of messes of its own making]] are finally gone]],’ Xinhua wrote.
It’s an interesting fact [[[that, <<compared with other countries, >> Australians are not very heavy drinkers]]].
The alledged (sic) fact [[that a motor breakes (sic) more easily under moderated modifications]] isn’t a symptom of anything going wrong with it –# just that the stock setup/tune is closer to its limits than it used to be.
No one would like to contend the blatantly obvious fact [[that thought and consciounsness (sic) do not fall into the category of material objects according to the current definitions of matter]].
These often correspond to comment Adjuncts in ‘declarative’ clauses (e.g. interestingly, Australians are not ...); but unlike statements realised by ‘declarative’ clauses, facts are not open to direct challenge in dialogic interaction.