I agree. I was tempted to put "It's a small world" but I was afraid to lose a heart. It would be nice to know if people use this phrase in Spanish the same way it's used in English - like when you move to a tiny village on the other side of the world and find out your next door neighbour is the guy you sat next to at school.
I agree that 'It's a small world' should be accepted as it sounds more natural and is a well known expression in English. It was the first option I thought of but I went with 'The world is small' which doesn't sound as natural becasue I figured a literal word for word translation would be what they (incorrectly) want.
I think that this translation is taken from an an attraction and related song at Disneyland-- It's a Small World-- Es un Mundo Pequeño.. See for example,
We don't usually say "tiny world"-- "small" seems to be the preferred adjective in this case. Even when people meet unexpectedly, for example, when I met someone from my US hometown quite by chance in Japan, we will often say, "Small world, isn't it?".
"Tiny" means "much smaller than small". One can say that a squirrel is a small creature, while an amoeba is a tiny creature. The Earth certainly looks tiny from far out in space, but in most cases we don't refer to it as "tiny". And if you want to emphasize "tiny" in Spanish, I think it might be better to say something like "minísculo" or "diminuto" or "pequeñito".