I fear I have to agree with tomdwil. There are always many ways to express something and even though you could just go ahead and only accept the literal translation, in my opinion this severely impacts learning by association. If the feedback to a contextually correct translation is negative this association - though correct - won't last.
I really would like "The book is mine" to be an accepted answer.
I think there are different types of 'literal translations'. For example, some users want us to allow literal translations for expressions like ha på sig kläder 'wear clothes'. A literal translation of that could be 'have on oneself clothes'. But when we say Jag har på mig en tröja in Swedish, that doesn't really translate into 'I have on myself a sweater' in English, because the languages don't work the same way. So in that sense, literal translations aren't what we're aiming for at all.
The book belongs to me however, is not a literal translation in that sense. It's just an exact translation of what the Swedish sentence actually says. If you rephrase it into The book is mine, you're doing exactly that – you're rewriting the sentence. And there's really no very good reason to do that in this case. It's not like it's any more unnatural to say 'The book belongs to me' in English than it is to say Boken tillhör mig in Swedish. As far as I can honestly tell, they're pretty much as perfect counterparts as any translations can be.
Also, the way courses are built here, we're pretty much teaching words after all. The association we're trying to get into your head is the same one that is in our heads: that tillhör and 'belongs to' correspond to one another. That's our goal here. Giving users maximal freedom of expression is not. This is the reasoning behind our choice of accepted answers here.
I agree, I personally find it hard to learn complex expressions in other languages if I don't know their literal meaning. In the course, you can usually find out what the literal translations would be (when don't also happen to be perfectly idiomatic translations, like here) by looking at the hints for each word. Or just ask in the forums if you aren't sure.
I thank you for that very precise explanation about the goals of Duolingo and the intentions behind the phrasing.
Though I would still appreciate a little more freedom in the expressions (not only here but especially in cases with "this/that" confusion) I also accept that it is not the intention of the course and yet again beyond the scope of the project.
Thank you again for explaining it in that way :) - and of course for the course.
I have also noticed that sometimes Swedish language spelling mistakes are not detected. Evidently it is a known thing at the Duolingo level, that this has gotten worse recently. If you have specific doubts you might want to look at the discussion page and see the spelling there. However usually Duo does notice spelling errors, and is forgiving of minor ones. That forgiveness might make the implementation more complex, causing these mistakes to pop up.