“We apologize for any inconvenience this may have caused you.”
The suggestion is that maybe some people might be slightly put out in some undefined way. But when the train is 40 minutes late, or your email has stopped working, I think that the people in charge know good and well that there’s been an inconvenience (at the least).
People deserve a little better. At the least, it should be, “We’re sorry for the inconvenience.” Better would be: “We know that you rely on us, and we’re sorry to have let you down.” You can follow that up with all kinds of assurances that we care, and we’re working hard to keep it from happening again, etc.
It’s all part of a sort of code of non-speak, where companies say things that would never fly in real conversation, but we accept. We hear that phrase and know that it means that something’s gone wrong, but we certainly don’t think of it as an apology (and it isn’t one).
I don’t like it, and I argue against it in my daily job.