Zero is an overloaded concept. There are at least like 5 or so different things that we use the word "zero" for, some of which are very sophisticated.
On the one hand, it means there's none of a thing in there. Most animals understand this. There is zero food here. There are zero predators on that island. Pretty sure crows have this one down pat.
Taking it one step further, you have zero as a number. Zero which is on equal footing as numbers like one or seven-- it is a number that you can perform arithmetic on or with. You can multiple by zero, you can add by zero, you can divide by -- wait, you can't divide by zero! The Greeks understood this. But lots of people say the Greek's "didn't have/didn't invent zero" because they used the word "nothing" instead of its own word. But Aristotle did say "nothing and nothing, added together, make nothing" and "there is no ratio of nothing to a number".
Crows probably don't understand that you cannot divide by zero. Maybe you could teach a crow that if two crows got ten total nuts, each crow would get five nuts, and so on. If you told that crow to split ten nuts between no crows, and ask the crow how many nuts each crow would get, the crow might tell you ten nuts, but it's not going to tell you that that operation is undefined.
Then there's the use of zero as a digit in a place-value system, like the one we use, as opposed to Roman numerals or Chinese numerals or so forth. Before there was a symbol for zero, you couldn't write one hundred and four as 104, it would just be 14 which was ambiguous. So when the Indians "invented zero" in the 7th century or whatever, it wasn't zero that they were inventing, it was the place-value system we use today to conduct our daily lives with, which is a shitload better than Roman numerals or trying to do arithmetic with a straightedge and compass or whatever.
There are a lot of people who claim that, for instance, the Maya were more mathematically advanced than the ancient Greeks, because the Maya had a symbol for zero (which looks sorta like a French baguette and an American football had a baby) and the Greeks didn't. While the Mayan way of writing down a number was much better than the Greek method, we don't have any evidence that the Mayans had much in the way of math beyond counting and extrapolating. The Mayans primary method of calculating is by drawing out tables: they knew the cycle of Venus is (roughly) 585 days, they knew the cycle of Mercury was 117 days, so you'd get a table with thousands of entries counting up the cycles. The Dresden codex has a table with 2340 entries, with 585 entries for Venus repeated 4 times and 117 entries for Mercury repeated 20 times. With a place-value system that used zeroes for zero digits. Which... ok, the place-value system was more advanced than the Greeks, but the Greeks would have done that same 'calculation' with a lot less tedium.
Then you have zero as in the additive identity, which opens whole new worlds of mathematics to you. Now you can start talking about things like rings, fields, and groups, and can have all sorts of fun. Pretty sure crows haven't sat down and discusses abelian vs non-abelian groups, but I wouldn't put it past them.
So anyway, any time someone starts talking about inventing or understanding the concept of zero but do not, themselves, display an understanding the concept of zero, (by explaining what it means in that context) it's generally a good time to stop listening.