Reasons for Using BBr3 for the reaction

-BBr3 has open shelled boron, and is very electrophilic. B can have 6 electrons and is stable without being
attached to a substituent during the reaction, and thus is a good leaving group since it is negatively charged
when attached to a substituent.
-BBr3 allows the reaction to react at room temperature* (as opposed to more extreme tempereatures required
by other reactants. In addition, the same article proves that BBr3 reacts more quickly (about 3 hours versus 7 days)
for the reasons given above.
-Other succesful compounds for demethylation reactions include HBr or AlBr3.
Both have experimentally demethylated 3,3-dimethoxy biphenyl but operate at much
more extreme temperatures (above 100oC) and often carry out side reactions. HBr
will default to acid base chemistry with a pKa of -9. AlBr3 will react with aromatic
compounds substituting Br for a hydrogen. Both reactoins occur via pathways learned in Chem210.

*McOmie, J. F. W.; Watts, M. L.; West, D. E. Tetrahedron 1968, 24, 2289-2292.