If you have reached an impasse, or if the adjuster fails to act promptly on your claim, politely suggest that the difficulties might be overcome if you both got another opinion. Ask to speak with the claims supervisor.
K stands for kosher the company is saying their product has no known products added that would deem the product not kosher. This doesn't certify the product kosher it just says the product is kosher style and no meat and dairy are mixed together, nor are there any animal by products added.
Dairy that comes from a Kosher animal is Kosher. Thus cow milk and goat cheese is Kosher, pig milk and camel cheese is not Kosher. Like any other Kosher food, it needs reliable supervision; simply because the package says Kosher does not make it Kosher.