No, it doesn't. It counts for the Rakghoul weekly which is not the one he's talking about. It needs to be in Tier 2. If both it and LI are on the same weekly quest and it doesn't count for the other Tier 1 HM weekly, then they need to be in their own Tier...
He said "the weekly" never specified which.
Rakhgoul Conflicts is THE
only weekly that matters as far as Flashpoints go