I think this has been resolved, to the most part, since Csharpd did the experiment for himself and heard the difference. Why his daughter thought the same (that a high D whistle is one tone above middle C, in his example) may have to do with the relatively complex harmonic pattern of the vibrations of the string (in the piano) versus the fewer harmonics audible in most whistles; she may associate the middle C on the piano with its higher harmonics and thence the confusion.
Csharpd mentions something else that’s quite important to the perception of pitch, and that’s timbre. Gosh, let me think of a good example from vocal music. OK. Take Tracy Chapman, who is a breathy alto. Think of how she sounds. Now, if you listen to her sing, it sounds like she’s singing quite low. Then take, oh, gosh, hmm . . . any one of the Three Tenors. Most of what they sing is in the same general range of what Chapman sings, but it sounds like they’re pitched higher. Even though they’re not. I think it probably has to do with what harmonics are the loudest.
As for the flute pitch . . . flute is one of the few instruments that’s traditionally not transposing. Meaning, you play a D, you get the same D in the same octave as what’s on the page. Whistle, meaning standard high D, is usually written an octave down because it’s easier to read when it sits nicely on one of the clefs (G clef, in this case) rather than on a bunch of ledger lines. If we were being REALLY retentive about whistle music notation, we’d put an 8 over the treble clef, signifying that all the notes are written an octave lower than they sound.
A transposed treble clef is most commonly used in vocal music by tenors, whose music is usually on treble clef written with an 8 underneath it, meaning that the notes are actually sounded an octave below what’s written. Classically-trained tenors, though, usually can read three clefs: bass clef (where the tenor part sits in a church hymnal), octave treble clef (where a lot of choral music is written), or even the dreaded C clef. C clef, if you never sang tenor or never played one of those middle-range instruments like the viola, is a WEIRD bugger. It shows you where C is, and you go from there. As you may not know if you’re self-taught, the circle in the treble clef surrounds G, hence the name ‘G-clef.’ The two dots in the bass clef surround F, so it’s also called the ‘F-clef.’ C-clef is like a double-loop which straddles C. C-clef is the least common and perhaps the hardest to read, since you can make any line you want C depending on how you draw the clef. But I digress. 
I talked about transposing instruments. . . by that, I mean things like the usual trumpet, which is in B-flat. So, when you see a written C, and finger a C, the note that comes out is a B-flat. There are C-trumpets, more useful for orchestral music, that play a C when you finger a C. But a marching band (or high-school band) trumpet transposes.
Just an FYI, since it’s sometimes confusing to hear people talk about an instrument in a certain pitch and wonder if it transposes or not. No matter what, uilleann pipe music is written with the bell tone on D. Strictly speaking, in classical terms, concert-pitch uilleann pipes are in C, C# pipes are in B, C pipes are in B-flat, and B pipes are in A. See what I mean?
For a B chanter:
Written note: low D
Note which sounds: B
so . . . for a written C, the instrument plays an A . . . so some folks outside the Irish tradition would call B pipes “A pipes,” because of that relationship between what’s on the page and what plays.
Confused?
Stuart
