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My impressions of free float vinyl is that it is the equivalent of a cheap replaceable carpet. I did the kitchen of my wife's office with free floating vinyl, since it was a small rented space and had low traffic. It worked fine there, but I can't imagine doing a new home kitchen that way. The refrigerator scuff, any heavy object dropped at an angle, any dragging of furniture, all of these will create damage. Even gluedown can be damaged, but the damage is usually nowhere near as extensive.
FWIW, our current home has glued down Nafco 16" square tiles and about a dozen replacement tiles for the inevitable. If one gets damaged, <shrug> oh well. I won't need to get stressed out, just pop the old tile and replace. BTW, the brown travertine pattern is by far the best I have seen for hiding dirt. I can't imagine anything showing dirt less. I've tracked in mud and not been able to see the footprints. The only telltale is the dirty mop water.
I think the builder went cheap, and got caught in a problem of his own making. If it were me, seeing how fragile the floor is, I'd have it ripped out, and sport for the cost of upgrading to tiles instead, and make them eat the cost of laying the tile. Why buy a known headache?
The best advice here is to NEVER move an appliance without a dolly or furnature straps. I have been installing vinyl floors for over 20 years and no floor is safe from the weight and bulkiness of a refrigerator. The weight of it alone will cause roll marks due to the wheels and thats even on a securely glued floor.