Broken screen whilst fixing the battery - Apple refusing to fix it

Took my phone in to get the battery replaced. When they started to do the replacement they stopped as the screen started to come apart, they asked me what they should do. Either to stop and put it back together and not replace the battery or carry on and risk damaging the screen all together. I told them to put it back together and not to do the replacement. When I came back to collect he phone they told me the screen was now unresponsive and wasn't working. They gave me a loan phone whilst they escalated the matter and that the screen should be fixed on their account. Only to find out today that Apple rejected the claim and will no longer fix the screen. I am now left with no phone and they want to me to pay to get the screen fixed, which costs basically the same as a new phone.

This is totally unacceptable. For a company as big as Apple to treat their clients this way.