From what I've read, copying a bunch of zeros to a device wouldn't be a reliable test. Drives that lie about their size sometimes have the non-existant storage mapped to lower addresses on the device. The file would appear to save correctly, but the later parts of the file would actually have overwritten the earlier parts - which won't be obvious if they're all the same. That's why you need to copy across a checksummed file. Stick with the ISOs, or use dd to create a file slightly less than 32GB and fill it from /dev/urandom.
dd if=/dev/urandom of=foo.bar bs=64M count=495
cp -n foo.bar /mnt/usb_stick/
should work, but I haven't tested it (no Linux boxen in my current location