Nitpick: it never was “just do whatever the underlying hardware does”. C standards try hard to avoid mentioning hardware at all (and, as far as I know, succeed at that), and there’s plenty of hardware that doesn’t do mod in hardware, yet supports it in C.
In C there are ton of things that are hardware dependent. For example the size of every data type is not specified, or the fact that char is signed or unsigned, the representation of signed integers (tough I don't think there still exist a platform that doesn't use 2's complement), ad a ton of other things.
I think there parent comment just meant that implementation dependent is technically not the same as hardware dependent.
For example, the size of int is not specified by the standard, as you said. But it can still be different from the natural word size of the underlying hardware, if the compiler vendor chooses to make it so. Case in point is int on 64-bit platforms is usually 32-bit in practice. In Microsoft's compiler, even long int is 32-bit even on 64-bit hardware.
Nitpick: it never was “just do whatever the underlying hardware does”. C standards try hard to avoid mentioning hardware at all (and, as far as I know, succeed at that), and there’s plenty of hardware that doesn’t do mod in hardware, yet supports it in C.