I wouldn't change the tense in the first case, as the sentence refers to a 'universal truth'. It was true when she said that, it is still true today, and will be true in the future (or at least as long as she's alive -- although ice will always melt if heated). As for the second example, I would only go one tense back if I knew that she was no longer working for the company.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.