CRC ERR! after battery replacement

My iPhone 5 got it's battery replaced at my local Apple Store through the Apple recall program - apart from the poor battery performance the phone was in good working order.

After picking the repaired phone up, I noticed that the battery charge indicator did not change and when I plugged the phone in to charge, it started a series of random re-booting (white screen and apple logo) - the error log shows repeated CRC errors.

Quick online chat with Apple, and they advise to take it back to the store as it is likely to be related to the battery replacement. Just come back from the store who insist that the problem is nothing to do with their repair and refuse to fix it. They insist that it must have been an underlying error that the battery fault was hiding, and that this error relates to a logic board fault that is nothing to do with the battery and therefore the technician who did the repair could not have caused this anyway, as they are separate components.

I hand them a phone apparently in perfect working order (apart from the original battery that they admit had a fault) - I get it back and it's broken: in my view they should repair it. What is my best way to resolve this with Apple? Is the store's explanation valid for this type of error, or is it made-up nonsense?

Thanks...