I think the implication is that without malloc you will remove a slew of potential bugs related to memory management, making the software more stable.
But no, judging from the code, you just give it one big fat I/O buffer that will usually come from .bss
It does eliminate a certain couple classes of errors, and makes some others less likely.
I didn't read all the code, but I don't think it's using alloca or the like. So the stack allocation sizes are known at compile time, and bounded unless there's some recursion going on (which is unlikely).