You are taking the relatives' words are gospel, but the relatives could be lying.
A funeral home who has stood the test of time by the local community has a lot to lose by lying about this.
One of my college jobs was working at a family-owned funeral home, and I don't remember ever any family being given any false information about caskets.
As a matter of fact, the funeral home will provide the clients with the address and phone number of the casket manufacturers if they wanted to compare funeral home prices versus ordering directly from the manufacturer.
Selling caskets was a very low pressure sales job, where most of the time, the funeral director will take the family to the show room and wait for them to ask a question. Many times the family will wander through the show room while the funeral director just stayed in a corner waiting for the family to inquire about anything.
my guess is they didn't want to keep the obese woman on ice while THE FUNERAL HOME waited for the delivery.
Corpes are kept in walk-in freezers that are working 24/7/365, so an additional day or two inside the freezer will not be a heavy burden.
Furthermore,if people ask for funerals to be delayed for unreasonable amounts of time (more than a week), they will charged for it, so there is no loss to the funeral home.
Finally, the "dying season" usually starts late in the fall and extends to the early in the spring; that's when the freezers tend to be filled to capacity. If this case happened during the summer, I seriously doubt that the capacity of the funeral home freezer was being stretched.
A family-owned funeral home with a long tradition at the local level is the kind of funeral home that I will use for my family and myself. That's why I find it out of character for a reputable business to be involved in the practices alleged by this family.
[Full disclosure: I do not work for any funeral home nor do I have any connection to the funeral industry. My college job happened years ago, and I majored and work in a complete different business]