It depends on the interpretation of "invent the concept of zero". It's not like suddenly, one guy invented zero and from that point on it was understood and used.

What your teachers were likely referring to and what the Indians were the first to do is write down a set of rules that defined arithmetic operations when zero is involved. Despite the fact that the included rules about division by zero were nonsense, this is the first recorded instance of someone attempting to "formalize" zero.

I didn't watch that show, but it was probably referring to something else.