A non-apology apology is a statement that has the form of an apology but does not express the expected contrition (Wikipedia).
We already discussed the importance to publicly apologize when that is the appropriate way to kill a crisis or at least to reduce damage. Unfortunately, public apologies often are not real apologies… For instance, they may be off-point, incomplete, defensive or self-pitying, or – even worst – formalistic and not heartfelt.
While apologies should always be timely, complete, unreserved, express regret and sympathy, accept personal responsibility and explain what one intends to do to help those affected.
Suggest to read an interesting analysis by Doug Pinkham, president of the US Public Affairs Council.