Why don't I say this once and for all:
Basically, the CFR requires the contractors to book lowest priced whenever available to contractors. So for the CFR purpose, BE is included. However, given that many contractors use travel agents, so BE may not be available to travel agents. Hence, it is not required.
But if OP will book his/her travel via the public website of an airline or BE shows up to travel agents, then indeed OP has to book BE.