The it's not possible answers are correct if you interpret the requirements strictly in light of the scene from the movie, where the fridge is directly exposed to the nuclear explosion. Having said that, your company could legitimately market a fridge that would be of benefit, within certain limitations.
1. The fridge would require to be installed in a cellar, or ideally in a reinforced shelter dug into your garden. At a time of heightened nuclear tension digging a shelter may be something people are prepared to do, similarly to how <PERSON> shelters were dug in many gardens in the UK in WW2. A shelter intended for nuclear use should ideally have a zigzag tunnel leading to it: the earth will provide a very significant amount of protection from direct gamma, neutron and thermal radiation.
2. The fridge should have a large dedicated compartment for fresh water, sufficient for an entire family to drink for at least a couple of days while you trek out of the fallout zone.
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The fridge should have a (non-refrigerated) compartment for other emergency supplies, particularly enough P3 particulate masks for the entire family. As above, these will be used during the first couple of days after the explosion while you trek out of the fallout zone, to prevent internal contamination. Other useful items: ear plugs (your eardrums will likely rupture thus providing a route for contamination particles into the lungs / stomach, so you will want to block your ears), disposable razors (contamination will be trapped quite effectively in hair so you will need to ensure everybody gets a close all-over shave, to reduce contamination), basic medical kit including splints and burns dressings.
4. The fridge should have a lead-acid battery backup, for when the power goes down, and beefy EMP protection.
5. The fridge should feature a pull-out strong metal frame so that it can serve the function of a <PERSON> shelter and protect the users from falling rubble if the building above collapses on the cellar, or the roof of the garden shelter falls in. It should also have a shovel and combination hammer / crowbar / wrench in case you need to dig your way out of the rubble.
It doesn't really work in the same way as the <PERSON> fridge, but I'd still be pretty happy to have such a fridge in a shelter in my garden if I was worried about possible nuclear attack. Obviously nothing would protect you from a direct hit, but the fridge would considerably enhance a shelter capable of supporting survival in the scenario you outlined as long as sufficient warning was provided to allow you to get into your shelter before the blast. 548