I don't think it's proved at all. "Ought" is an appeal to symmetry. At the same time I don't think that necessarily undermines the argument.
The dual numbers contain infinitesimal numbers but not infinite numbers.
Oppositely, the variable X of a polynomial behaves much like an infinity, but is not invertible.
Their argument depends crucially on whether infinitesimals/infinities are invertible.
It wasn't clear to me that the second sentence was sufficiently proved. At first glance it seems reasonable, but the authors went a bit too fast past that claim for me.