Cantor's diagonalization argument for example, when used to show that R and Z have different cardinalities. It's a legitimate use, but huge numbers of incorrect counter-examples (that are really just examples) surface around it using the decimal expansion incorrectly. And the decimal expansion used in the actual diagonalization requires some careful consideration, since you have to be careful to remember that 0.10000... = 0.09999... so decimal expansions aren't unique.
Your use seems fine (and dealing only with integers the expansion is unique), but most of the time when a mathematician sees someone using digits they get a sense of unease and wonder if there were a better way to do things.
I think that sentence is entirely true if you delete the word 'necessary', and otherwise entirely false. I think that almost everyone would agree that at the heart of modern cryptography is an application par excellence of modular arithmetic, but I think that no-one would claim that cryptography cannot be done without modular arithmetic.