I often hear people (especially policitians) giving an “apology” that is phrased so that the speaker does not seem to be accepting blame.
e.g. Instead of
“I am sorry I let you down”
“I am sorry if you feel I let you down.”
I’m sorry if I let you down.
Can these be considered apologies? In the first, the speaker almost sounds to me as though he is feeling sorry for you for (mistakenly) feeling that he let you down.
In the second, the speaker doesn’t seem to be acknowledging he let you down at all.
There is a wikipedia article on non-apology which goes into some further detail.
In actual use, even though these conditionals are not really apologies, they can still be honestly used if you deliver them sincerely.
Though I would use these only in the cases where it is not clear where the guilt lies, to express recognition that I might have caused offense. The difference is that in this case I want to express that I am sorry for the outcome and not necessarily for the action that caused it.