Is it any worse than any other residential dropped beam? I have a lowered ceiling (not shown) on the left side flush with the bottom of the beam if needed to resolve the torsion. Just curious of other's thoughts w/o the ceiling.
If it was very highly loaded I might but not in this case. I'd make sure I had a reasonable load path to resolve any torsion at the columns ie. full height bolted to the dbl top plate. I also wouldn't design the beam to 99% for stresses.
As it is it looks like most of the torsion from the wall and joist load cancels out. Though I don't think I'd worry about it even if the rim was flush with the left side of the nailer.
1) You've no got automatic torsional restraint built in
2) The joists do not make it past the beam centerline so rotation of the beam cannot entirely shed the torsion in the act of twisting.
I would probably take a quick look at the lateral deflection of the bottom flange as a girt element and see how I felt about that. If that's minimal, I'd be inclined to not fuss over this.