It would have taken just as long to pick up the book and glance at the back than it did to snap the pic. They then posted it later without even a cursory search online. It's a post to garner attention. If they had any real conviction they would have investigated it. Swastika = bad, please "like".
The fact that it's an instant take rather than well-thought out is the whole point; it's a snapshot of someone's life in a single instant, not a biography. I think there's value in that, even personally it's not my natural mode. When you post in this way, you're gonna have some egregious misses.
Yes, he posted on Twitter a quick reaction to what he saw, i.e. did what millions of people use Twitter for. Expecting a kid to investigate everything he posts on his personal microblog is… lol.