I think that's just a mistake on her part. She is playing on both the E and G string around that particular F string, she only hits the F string twice, and the second time she hits it, it twangs - my guess is she missed it the first time and tried to correct it for the second time but missed slightly, hence the twang. She doesn't play it again after that.
It DOES reveal, though, that she leaves the F pedal alone, but I still think the piece implies G-flat major (with the assumption that the F would be TECHNICALLY natural, but since it's never played she just left it flat).
There are other places where she does this - the only example I can think of from the top of my head is in Have One On Me, during the "Ooh ooh" section. It's tonic is technically a B major chord, but because the progression is B major - D major (as opposed to D-sharp) - A major (as opposed to A-sharp), a couple things are implicated:
-the only time an A is played is during the A major chord, so the A pedal will be set to natural the entire time and not moved - this is also useful since all the As in the preceding and following sections are natural
-the D is natural for the D chord, but must be sharp for the B chord, so the D pedal is toggled
-F pedal is sharp for both the D and B chords and from the last chord of the previous section, so the F pedal is set to sharp and doesn't move
-C pedal is sharp for the A chord, and all Cs in the following section are sharp, so it is set to sharp and doesn't move
-No G is played in this section, but it is played as natural in the last chord before this and in the first chord after this section, so it is left in natural position
-Also, the flatted seventh (the A chord) implies B mixolydian mode, but the flatted 2 for the D major chord suggests either B dorian (except the Ds are sharp in the B chord), or that the D major chord is really V/bVI - not that that matters, but analysis is fun, and I think it is borrowed!
SOOO... knowing all those things - where you are going, where you are coming from, what notes are present at what aren't, the "Ooh ooh" section of Have One On Me is TECHNICALLY grounded in B mixolydian (because of the A naturals) with a borrowed chord (because of D major chord), but the PEDALS are set to D major - F# and C# only, with a toggling D pedal. This makes the most sense since the section after it, the swoopy arpeggios, is in D major and it would be the easiest pedal change to make, AND the chord just before this section starts is a Cadd#4 (C major chord with an F-sharp). That means that all she has to do is kick the D pedal to sharp for the first chord and kick the C pedal to sharp sometime before the A chord - which she has 8 beats to do. And after that, it's just a movement of the D pedal and nothing more. And when she gets to the swoopy section again, all she has to do is take the D pedal back to natural.
I love puzzles : ) But it's also convincing me that the F-flats in that Bridges & Balloons video are just an accident, and were probably left flat because there was no need to change the pedal (though maybe after this little accident, she started setting it correctly JUST IN CASE...
).