Your comment "you often need to think about the contents of your statement" is VERY accurate, and your internet resource has given an excellent example of who people don't think about the contents. The resource has considered the wrong aspect of this sentence. It's these inappropriate examples that cause so much confusion when punctuating. The consideration here is the 'subject' of the sentence.
The reason a comma is not used before "because" is because the subject of this sentence is "I knew", not "President Nixon would resign that morning"
To explain ...
What this sentence is really saying is I knew that 'insert information' because my sister worked in the White House, and she called me with the news. You can clearly see in this case that you would not place a comma before "because." However, in both cases there should be a comma after house as she called me with the news is an independent clause.
The very use of "because" dictates that the following clause will be sub-ordinated in every case, and sub-ordinated clauses are not separated by commas.
I hope I have explained this well enough to clarify your confusion. In short, never use a comma before because*.
**Disclaimer* unless the writer is being 'creative' and knows the rules he/she is breaking