Win7 32-bit (x86) has less memory overheads as the pointers are half the size.
If you only have 2GB, 3GB or even 4GB of RAM you may end up with more free memory.
99% of Win32 processes are limited to just under 2GB anyway.
Maybe he has a piece of hardware, or software, that just does not work under x64 without resorting to more technical configuration changes, etc?