Do you think people would not understand if he were to say "a baby koala" instead of "a baby koala bear"?

I would guess that most people would understand.

so why can't he just use the right name?

A name is just what we decide to call something. In much of the USA, the name given to that animal is a koala bear. I grew up hearing them called koala bears, and on the very rare occasion that I hear them referenced now, they are usually called koala bears. It is technically incorrect, for sure, but that is what it is called. There are other examples, such as the "gray fox," which is not taxonomically a "true fox." A difference is that it may still be considered a fox by all by the most strict taxonomists since it doesn't fit nicely into another group (like the koala does).

Another example is that I often hear people say they are going to an "ATM machine" even though the "M" stands for machine. I do not think it is stupid to say "ATM machine" since that is the common vernacular where I am from. It may be true that some people call it the ATM, as it technically should be called, but that is simply not common where I live.