There's a story about the young Edmund Rubbra, which goes something like
this: He was going to visit some friends with his parents.  They couldn't
remember which house in the street they were going to, whereupon Edmund
piped up 'I know which one it is - when you kick the boot scraper, it gives
a G sharp!'

Sight-singing involves (for me at least) mentally imagining the pitch of
the first note you sing before you sing it.  I don't have perfect pitch,
and when asked to sing a given note from cold will only be accurate to
within a tone or so.  I am even worse at saying what note an instrument is
playing.  However, I'm very sensitive to singing notes at other than the
written pitch because I know how it feels to sing each pitch - sufficiently
so that when our church organ at about A=436 was temporarily replaced by
one at A=440, I had to make a conscious adjustment to my technique to sing
with the new instrument.  When choirs drift down (or up) in pitch or music
is transposed, I make the appropriate technical adjustments.  It's harder
if I haven't warmed up and got a feel for how my voice is performing that
day.

I can tell fairly easily whether choral music performed by others (at
least by British choirs) has been transposed because I know at which
pitches choral tone changes.  I suppose that if I acquired equal
familiarity with instruments I might be better at identifying their
pitches too.

Perfect pitch doesn't always go with musicality in my experience.  The
person with the most finely-honed sense of perfect pitch of anyone I've
met was not very musical in other ways.

Virginia Knight
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http://www.ilrt.bris.ac.uk/~ggvhk/virginia.html