Be persistent
I have just been through this exact problem with Applecare. My home key was unresponsive and I was told by a "genius" at an Apple store that I had clearly submerged my phone as both indicators had been tripped. I knew this was not the case, though my iPhone had been used extensively on dog walks and whilst exercising (are they not designed for these purposes?).
I contacted Applecare, after 45 minutes on a premium rate call I explained my problem to a senior advisor, who eventually authorised a return for inspection. They found that the internal indicator had NOT been affected, it had not been submerged, and a replacement phone is being shipped.