I call bullshit on this bullshit. When my systems go down, I AM sorry if it inconveniences my users. Why is this not OK? It beats the hell out of some stupid-ass whale picture.
But there is a difference between an outage on a free service and a paid service.
I think 37signals write about that themselves, and how they get away with 95% or something.
Then again, I think being cold and going for the "we apologize for any inconvenience" line can have some advantages over being personal - it implies you are more objective and reliable.
Just say what went wrong, how you're dealing with it now and in the future, and what you're doing to make it up to everyone that was (potentially) affected.
If someone writes back with a specific incident caused by the outage, you can address it directly then.