One of the things I never leave home without is my "Travel Companion" which has an alarm clock, flashlight, smoke detector and motion sensor all in one. I've had hotels miss wake-up calls more than once, and learned my lesson - it's ultimately up to me to get myself up in time to get to where I need to go.
Yes, the Doubletree erred. Even four-star hotels make mistakes. They know this and have comped you your extra room night and meals. I'd consider this adequate compensation for a missed phone call. When you get home, go shopping for a travel alarm clock. Hope you enjoyed your trip otherwise!