You never have to accept an extension. I had one of the crafters of 117 on my JS a while back. He said the airlines are purposely misinterpreting the reg for their own gain.
Also ALPA, at least at my airline has done a miserable job of making pilots aware of this. Same with the rest rules. The reg states "8 hours of uninterupted sleep opportunity". Unless you sleep in your uniform, don't brush your teeth or shave and can fall asleep on command that means about 9 hours behind the door. I have several times used this and told the company I'll be at pickup at this time because of it. Never been questioned on it, but if they did give me grief I feel confident the reg would back me up.