I believe the claim was days and week(singular). It is true. Tornados, hurricanes, heavy winds, ice storms, snow storms, etc. I have had my power go out for days at least once in the last 10 years. I don't think there is a year which goes by where there is not multiple instances of areas around here loosing power for days. Most of the areas are not what I would call rural either.
I can't say I have ever experienced a situation where I could not drive a short distance and pick up gas. Even when I was without power for days, there was no issue getting gas.