Bridging vs. Routing Firewalls.

[Georges J. JAHCHAN, P. Eng.]

A manufacturer of bridging firewalls (which are also capable of operating as static routing devices) claim that using their firewalls in bridging mode is more secure than in routing mode. Their reasoning is that in bridging mode, the device's Ethernet interfaces do not need to be assigned IP addresses, thus the box itself is immune to hacking. Also, any MAC address which moves from one interface to another is blocked, until cleared by the administrator (though this feature can be disabled). Is there any truth to the claim of a higher level of security (all else being equal)?