Good morning Vickie, 
My understanding of the (brackets) is that it marks a parenthetical sentence or paragraph. It isn't that it was an addition, or a translators thought, but that it was placed in an incorrect spot. I was thumbing through the Bible to find where an entire chapter is a parenthetical chapter showing it should be placed either before or after another chapter. I haven't yet found it but I'll let you know if I do.
The words printed in italics are changes from the text...additions, etc. and could be discarded.
In the kjv they have asterisks by a word that is added and some words they did not mark them, in the NIV it has been the parenthesis...it is interesting what you say in your quote above...that an entire chapter would be placed in another place...that doesn't sound good..as the words of the Lord are not to be changed out of sequence they have been given..
I'm a KJV girl. In it the additions are shown in italics and I, as you, tend to discard them. To my knowledge the () doesn't denote an addition. The Bible I use, a KJV, Companion Bible - E.W. Bullinger, notes additions, corrections, etc. No notice was given on the verse we're discussing as being improper.
It is always nice to have others researching to on matters I will share a little on the NIV which I love deeply and use..
In the 1978 edition revised 1983 in my book it has the comment; "as an aid to the reader, italicized sectional headings are inserted in most of the books. They are NOT to be regarded as PART of the NIV TEXT, are NOT FOR ORAL READING and are not intended to DICTATE THE INTERPRETATION OF THE SECTIONS THEY HEAD... Prefaces page xiii
The headings I have noticed at the beginning of some chapters does not fit the contents of what is being spoken about in that following chapter and the heading should not be there..they NIV was correct for writing the disclaimer..but still they should not have added the sub-titles as even that is against the Lord's command...I am also looking to find the paragraph that speaks on parenthesis being used in the NIV I use...
Thanks again and I am glad you are seeking for truth in this as well.
In Christ's love