I don't agree that this is what sympathy means, but I do think that lots of people get in a cycle of toxic behaviour where all they crave is sympathy or empathy, and they fail to empower themselves to fix their own problems.
Yeah, that's just not what the word sympathy means. You're not feeling sympathy when you shirk off someone else's problems. That's the literal opposite, so I really dislike that video. "It could be worse" is not a statement of sympathy, it's a statement of indifference. It's what we tell ourselves when we want to care less about something bad. Not what we expect from telling someone we are asking for help from.