We have several of this type of installation. I can tell you what the practice is here.
You own the disconnect switch. You own the transformer. Both are on your property.
The service is at the your disconnect. The transformer is an SDS. The design of the grounding and bonding is up to you and the NEC. It doesn't matter where the metering is - that's just a contract issue.
Translating your question: If the utility owns the transformer, they want to separate the grounding of the transformer form the grounding of the facility. The only connection between the two grounding systems is the earth. What would that gain the utility? Why would it be different if the transformer were customer owned?
Only one reason I can think of. If the utility owns the xfm, then the NEC (for solidly grounded systems) requires the system be bonded at the forst disconnect. And of course, the utility bonds at the xfm. So with a fat ground mat between the utility xfm and the facility ther is a parallel path for the neutral current. Bad Science, but meets the NEC. So, the utility likely tells the customer to separate the grounding between the utility xfm and the facility - so there is no parallel path.
If you own the transformer, there is no problem. The transformer is an
SDS. The NEC requires you to bond the system in only one place - the xfm, the disconnect, or anywhere in between. Much better science.
My recommendation is to connect the grounding under the service disconnect, transformer, facility all together. Bond the xfm secondary at only one place. That is good science - good engioneering
carl