There's a story about the opera singer Kirsten Flagstad (1895 - 1962) from when she performed at a small place somewhere, singing opera songs with just a piano. Afterwards one from the audience actually complained directly to her that she didn't sing well, she was out of tune. She apologized and said that she had perfect pitch, and the piano wasn't tuned to her inner pitch - and she found herself unable to adjust to the piano.
As for singers in general, I've seen lots of professional singers who don't have perfect pitch but still can cold-start a song - they know their own vocal cords so well that they can start at the right pitch with confidence.
As for singers in general, I've seen lots of professional singers who don't have perfect pitch but still can cold-start a song - they know their own vocal cords so well that they can start at the right pitch with confidence.