What does processor but width have to do with the likelihood of allocation failures?

I think what he means is that on a 64-bit system you have a massive virtual address space (typically only 48-bit, but that's still 256TB), and since malloc allocates from virtual address space, not limited by physical memory, it is unlikely you will get a malloc failure (unless you are trying to allocate more than 256TB per process, maybe due to a memory leak).

640K ought to be enough for anybody!