... They don't want to run the trunks through the same NIC as the phones...
Why? This makes no sense at all, it is literally how it is designed to work.
In fact, this would cut down on traffic load through the Mitel controller... Right now all calls in or out of the system have to go to the controller, then be transcoded from IP to TDM and sent to the PSTN via the PRI. WIth SIP trunking, assuming you don't have a call recording server or something like that, the audio goes directly from the handset to the MBG (or other SBC) and only control signals go though the controller in most cases. It is literally easier for the system and reduced IP traffic to the controller when using SIP trunks, in most cases.