The guide I have is called "Mitel 5312/5324 IP Phones. SIP User and Administration Guide. Release 7.2 UR1" (April, 2009).
Moreover, official documentation on Mitel site for Web Configuration Tool, which is used to web-access and configure the SIP phone, claims the same. It says that Mitel 5312
supports BLF, and that a key on the phone
can be programmed to use BLF.
I emailed to Mitel's sales department and they replied:
The documentation that I have for the 5312/5324 shows that you may be able to program your phone for this feature. Unfortunately, it does not give any steps to do so, you will need a programming guide for that. Your Mitel representative can help with the instructions. If they are unable to clarify or confirm this for you, contact Customer Care at 1-800-722-1301.
My local Mitel reseller can only confirm that they also don't see this item on Mitel 5312, but it appears on Mitel 5330. Unfortunately, I'm not registered at Customer Care and they couldn't open a ticket for me. Is that how Mitel technical support works? They claim features they don't have and can't even confirm or explain it.