LH2 - Not sure I would agree with the word "significant".
You will have sticker shock compared to your local store no matter what since all the food is shipped in.
The question comes down to 1) Do you have the time 2) Do You want to go shopping yourself.
Some people think it's a waste of good vacation time or are rushed to start the charter, so it's worth the extra few $$$ but it does not cost 50% more to pre-order.
I always enjoy shopping on all the different islands especially when I can go to open fresh markets even when I can't speak the language (ie; french) as you really get to experience another side of the local culture.
However, You WILL save a ton buying from the grocery/liquor store(s) (online or in person) compared to provisioning from charter company.....maybe that's what they meant?
Here are a few more links:
Traveltalkonline: Provisioning - "free delivery"
Provisioning