Sure it is- to an extent. It's pretty hard not to be self obsessed when you're sad though. We're sentient beings that have heightened awareness of ourselves and the space we live in. Some of the things that happen in our lives are deeply unpleasant.
Someone we care about dies, we become unwell, something we've worked very hard to achieve at, we fail in, someone says or does something cruel to us. Those things- surely rightly cause us to be unhappy. Maybe the real problems occur when we can't bring ourselves out of that emotion. So, we almost become obsessed with the emotion itself. We notice all the time that we feel sad.
That's surely a question a lot of people are asking themselves througout the day though: 'How am I? Does anything hurt? Does anything need fixing?' Surely, that's how we self regulate. We're constantly aware of our needs. Am I hungry, thirsty, too hot or cold, how am I feeling? I think we're maybe 'fixers' by nature. We look for problems and try to fix them. When we can't though, we get kind of obsessive about it. Like- shit- I'm still unhappy. What can I do about it?
Plus, if it gets too bad, we may reach a point where we find it difficult to work. Difficult to find the energy to look after ourselves. So- with less task based activities to occupy our brains, they likely will obsess about our sadness even more.
Plus, I think we can start to find a kind of comfort in it. Feelings of sadness, apathy, lethargy can also lead us to not challenge ourselves. That can feel like a nice break if all you've been encouraged to do in life is push yourself, face your fears, take risks. It can be nice to let yourself off the hook as it were.
What's the alternative though? Distract ourselves by obsessing over something else? Work? Who does that benefit? Our (likely fairly heartless) pay masters. Relationships? Too much obsession towards another surely leads to things like codependency, which isn't healthy either.
I think more though, there's this assumption that if only people live a more 'normal' life. Where they interact with others, have a busy schedule, have lots of things to think about- that will stop them being sad. I know from experience that it doesn't though. You simply get home from work, exhausted from the day itself and having to put on a facade and just cry your eyes out!
I remember Stephen Fry talking about depression and those doubters who say it isn't real. He compared that to someone standing in a rainstorm but swearing that it wasn't raining. Surely- we're either sad or, we're not. Maybe there are things we can do to move ourselves beyond that emotion but, maybe not always.