We've seen different PLA units receiving what seems to be personalized & highly-customized gear, so it is definitely possible that some procurement decisions are made at such levels of command. It makes sense too, since different units face varying conditions & operational requirements.
If enough troops and/or commanders voice a common concern regarding a certain aspect of their equipment, that request is usually heard at the top; this is common to almost all professional & organized militaries.
Yes, I mean obviously having variations of different gear and customized gear is present in the the PLA in different units, but I'm not sure if that would extend all the way to seeking development of an entirely new weapon like a LMG or HMG.
I can certainly see more specialized units like SOFs to be able to seek more unique variants or even entirely new weapons intended for themselves alone, but things like LMGs, HMGs or for that matter a new assault rifle family, seems like it would be a decision made at a much higher level.
I'm not saying your suggestion isn't true, but I'm skeptical that requests for new designs of an LMG or HMG could be done independently at the brigade or even group army level... not least considering how much the PLA itself needs a newer LMG and HMG