Per TopBunk:
The fuel pumps in the 777 are not engine specific and the architecture differs from that on other aircraft, ...
I infer from this that the LP pumps (aircraft side) are implicated, and not the HP pumps (which are certainly engine-specific).
However, it
may also be that the specific R-R HP pump is somehow more susceptible, compared to Brand X or Brand Y, to whatever LP-side shortfall may exist. Time will time I hope.