That was my intended point to the original poster, but stated more-or-less in reverse. If a C-E-G triad appears on a D-signed staff, then it is no longer a C-E-G triad. The C may not have the sharp symbol beside it, but it is there at the beginning of the line.

He seemed to be saying that a C-E-G triad becomes different chords depending on the key signature.

But this all may be more semantics than music theory.