Telling someone whose animal you've never seen that they need to put that animal down isn't politically incorrect. It's rude. There is a difference.
And it's hurtful to someone who is already facing the pain of losing a beloved pet in the near future. Euthanasia is a heartbreaking decision that people who know and love the animal need to make for the animal. There are differences in people, but also differences in animals, due to temperament and constitution. Some animals with a given set of conditions may be miserable, others might be happy. Pain control may be good in one case, impossible in another. Insisting that you know what is best for an animal you've never even met, is an indication that you have no idea what you're talking about.
There are certainly times and places where asking the right questions and helping someone to look at what is going on is helpful. Telling someone they are wrong because you know more than they do about an animal that they live with and you've never seen, is not helpful.