I was taught that it was. The textbook I used was Axler's Linear Algebra Done Right. And

wiki seems to agree too.

But for a perhaps better reference, here's an entry about the zero polynomial on Wolfram:

Zero Polynomial
Looks like it's either undefined, $\displaystyle -\infty$, or $\displaystyle -1$. I'm pretty sure it can't be 0 though .. not that I'm an expert or anything.

I meant that through the post about the degree of the zero polynomial and the OP's post which contained a counterexample, it should all be clear now.