If you're reading a book can your brain make you read a sentence that isn't actually in the book, also can this happen if you're reading an online article? Also if you went back to the source would you see the same faker sentence? How could this happen? Due to stress or over thinking, or what?

It is not really falsify information as much as it expects to see and may think it sees it.
For example, take a poem or something you may have repeated 10,000 times, I used to say Plead of Allegiance but most Americans don't know it any more
Leave out two or three words and read it, you will read it the way you know it.
Same with a few words, many speed readers don't read every word, but scan and leave out the "the" and the "an" and other words.

It is similar to the mental tricks where two lines look different lengths but are the same and so on. Just tricks the mind does some times.