I agree with David - if you have the information you need to investigate a claim then you (or your vendor) must proceed. I state it that way on purpose because while you contract with your vendor, you still have the ability to conduct an investigation on your own. This may not be a prudent or even doable given how much free time you may (not) have but it is an option.
However, while you must perform an investigation, if you advise the customer you require the dispute to be in writing then you can withhold issuing credit upfront if a written response is not received within the time limit given in Reg. E (10 days).
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My opinions do not necessarily reflect those of all the voices in my head.