I agree with you Beersmith. Having had ,in the past, experience in dealing with major supermarkets, I can conc ur that the management treat all lower tiers as if they were themselves compostable. However, it would do no harm to pursue this through the tier, just ask for the names of the immediate heirachy, mentioning that you will remark upon their willingness to assist.
More likely to succeed would be a request that they permit you to collect 'vegetative waste, card etc' so that you can make use of it for your composting.