First, unlike other SA, West Point does not put any points towards your interview when totaling your WCS. The FFR does not have a primary role in the selection process that is meant to be as objective as possible. With that said, your FFR can have a positive effect on your chances in that their support will keep your file on the mind of the RC. Because of how the selection works in accordance with Congressional law, it can't make your RC chose you for appointment over someone else if they meet all the qualifications. It can in the case of non-selection boost your chances of getting a civil prep offer. On the negative side, if you present yourself poorly to your FFR, that word will get back to your RC. Instead of looking for how to best support a qualification, they may look for ways to disqualify you. These cases are very rare. Most of the applicants present themselves very well to their FFR. Think of it as a bell curve - if you are in the middle, no real impact. If you are out on either tail, it can really help or hurt you.
Second, the primary role of the FFR is meant to be a guide through the process and to be a mentor. They are there to be a local contact you can turn to for support/advice on the admissions process, life at West Point, and service in the Army. Of course, each has a different perspective (recent grad, old grad, parent...) and different amount of commitments (as volunteers, they can easily be overcome by their own work requirements, or might be filling a really large area that keeps them from being the most responsive). I think this is where the FFR has their most influence - helping the good candidates get through the complex process in a manner that has proven successful in the past, helping candidates decide if a service academy (or even service) is right for them, and steering bad candidates out of the process (or at least making sure that they focus on Navy instead of West Point). They also become the link to the parents club so that Mom and Dad have an outlet to ask their questions to.
Third, given all the above, often times FFR will sit on a MOC's nomination committee and then they have significant influence in your chances of an appointment. A good FFR that is on a (or several) nominating committees can work with the representative to maximize the use of those nominations to get as many candidates as possible into WP. Then, if you are that candidate that is really strong, but maybe not so much on paper, your FFR can help you gain an appointment by swaying the MOC to give a principal nomination.
So onto your second question of how accurate your FFR's statement is...and the answer is it depends: when did they tell you that/when did you complete your file, how many candidates that you are competing with have finished since, how much have you updated your file, how knowledgeable is your FFR (you may be the strongest candidate they cover in their part of a district, but they don't know the other candidates you are competing against)... As always, the LOE is a good sign, but it is not a guarantee. There are too many variables that go into how West Point MUST select a candidate to boil it down to one thing is a make or break. Patience and a solid Plan B is the medicine to calm your nerves at this point.