Not really true, but I guess it depends on the country.
In the United States at least, burning your own book, flag, or whatever is legally protected free speech. Just as long as you aren't destroying someone else's property.
Context also matters. Burning bibles during a religious service is probably a thin line.
How about no burning anything in public? It's a stupid thing to do and proves nothing, risks starting unintended fires, or people injuring themselves, etc.
Burning stuff is a classic protest move though, and that shouldn't be restricted either - within safety limits of course; i.e. Don't leave your burning flag, book, bra, whatever where it might destroy unrelated stuff.