The only thing I can ask you after reading this post is, Would you buy a note just by the third party grading?
What I seem to find with a lot of the dealers at shows is they have the same notes graded by an American third party grader show after show, which in my opinion means that they are not selling them very often. The best thing to do is get a mentor that understands how to grade and teach you how to grade your own notes before you buy them. If the note is graded by a professional grading company DOES NOT mean thats what grade the note actually reaches. Sometimes they are right on , sometimes they are way off.
When dealing with a cheaper note for your collection its makes a difference but you won't lose a pot full of money, although this would not be the case for a rarer note that a single jump in grade could run you up a few thousand extra.
I was lucky and became friends with a very experienced collector that showed me how to grade my own notes, I even make mistakes but can do quite well in most cases
. I have had sent notes to BCS to have them graded but it was not to get a grade assigned to them per say but to get them into sealed protected sleeves that the note would have a hard time being damaged when I have them at home.
So my main advice to any collector to protect your investment is Learn How To Grade and don't get taken from a note in a sleeve that someone else has thrown their opinion of whats inside.