I read that part as the assembler itself never freeing memory during its work assembling. The assembled program can do whatever including using the stack and manual memory management.
I wrote a crude assembler in Pascal once (for fun). It didn't need a heap, it was all static allocation and stack - it didn't cross my mind that one might write an assembler that needs to do heap allocation. I was a callow youth, and probably didn't know what a heap was!
The only storage you need other than stack is for a symbol table. In the general case, you can't know in advance how big that's going to be, so I suppose heap allocation for the symbol table makes sense.
