Very wierd response from member services. I'd call bell services at the resort you are staying at.
We moved from the GF to the Boardwalk last year & the groceries were colder than when we had them in our fridge. I enjoyed a beer immediately as a result.

They even took special care of my DM's b-day cake.
I wonder if they are having TOO many split stays lately b/c people can't get into the resorts they want for the whole time. Maybe if it's a busier time of year they won't do it. Or maybe just more people are using outside grocery companies. Maybe they just don't want the risk of moving people's eggs.
To the OP:
Have you stayed at a value resort before?? After being spoiled by
DVC for so many years, have considered a moderate or the Swan & Dolphin who often have deals going? But that's just my humble opinion b/c we had such a terrible experience at All Star Sports. Out of control tweens/teens were ding dong ditching us & the walls seemed paper thing. Even w/ earplugs I got very little sleep. The place was packed.