Not necessarily (dependent on the type of semiconductor used to store the ROM information, but it's usually Flash ROM, which as a type of EEPROM).
Specific code may be all that needs to be replaced, so they may choose to rewrite data for specific addresses on the ROM instead (keeps the .bin file/s smaller, which tends to help the download servers). Flash ROM allows for partial re-writes, and is cheap as well (why they use it).
For example, the firmware in say an Areca RAID card is in 4x different sections, and depending on the user's requirements, may not all need to be updated (i.e. changing BOOT.BIN to EFI.BIN when you want to boot off the card in a Mac Pro, but otherwise nothing else needs to change).