Because it synergyses with the supression ability, mate.
Giving a weapons to RE is not always a good strategy but their are some benefits:
1) It replace a weaker weapon
one Re + one Riflemen have 4 carbine + 5 m1.
Giving a BAR:
to Riflemen 4 carbines +4 M1 +1 BAR<to Re 3 carbines + 5 M1 + 1 bar
2) Re have an accuracy bonus at Vet 1
3) Force opponent to make a choice to either focus fire on Riflemen and be fired upon by bar or focus fire on RE and be fired upon by m1.
In sort one can gain an early advantage by it.