The fact that is a common construction that has gained some uses outside its original one;
it's now also widely used as a hesitation particle before a tensed clause.
I.e, instead of saying
- He was told that the meeting is Wednesday.
one says
- He was told the fact that the meeting is Wednesday.
But this does change the meaning,
since the NP Complement -- the that-clause following a picture noun --
of fact is Presupposed, not merely asserted.
(That means the speaker takes responsibility for the truth of the that-clause,
and expects all listeners and readers to assume it also, without question.)
As to whether that can be deleted, normally the that's necessary to mark the clause as an NP complement, which is not a terribly common construction, and therefore might not be obvious.
- the report/story/rumor/claim/belief/fact that Congress has passed the Antarctica Bill
- *the report Congress has passed the Antarctica Bill
- *the story Congress has passed the Antarctica Bill
- *?the rumor Congress has passed the Antarctica Bill
- *?the claim Congress has passed the Antarctica Bill
- *the belief Congress has passed the Antarctica Bill
- *the fact Congress has passed the Antarctica Bill