>>It IS clearly pinkish, but it doesn’t look pink colored when it is first handed to her. ???<<
It looks pink in the views where her hand is behind the glass. The pink tinge is very likely due to her hand showing through the plastic glass. I don’t think they’re dumb enough to hand her water that looks doctored. That said, as I explain in my next comment, it might very well be doctored.
Maybe she is bleeding in her mouth. That would explain dark red lipstick to hide the bleeding.