***** NOT A TEACHER *****
1. This is how one of my favorite books would explain your sentence:
a. "I want to make sure of this fact (that the article has been proofread)."
i. "That" introduces the appositive "the article has been proofread." The appositive explains what "this fact" refers to. As you can see, the words "of this fact that" are not necessary.
2. Now look at these two sentences that I have made up:
a. "I know that Yslamac is a good student."
i. Another of my favorite books explains such a sentence this way:
(a) "I know that: Yslamac is a good student." The object of "know" is "that." And "Yslamac is a good student" explains what "that" means. But the English people started to feel that "Yslamac is a good student" was the object of the verb "know." Thus, "that" was used ONLY to introduce the noun clause. So in ordinary speech and writing, it can be deleted.
(i) "Everyone says (that) Yslamac is doing very well in English."
James
Authorities: House and Harman, Descriptive English Grammar (1950).
George Curme, A Grammar of the English Language (1931).