You can apologise *for* something, but can you apologise *that* something?
Solution 1:
From Sorry About That: The Language of Public Apology by Edwin L. Battistella
That versus If
It is also possible to use a noun clause as the direct object of apologize. There are two main types. One begins with the word that and introduces a presumed fact (grammarians call it a factive clause). Someone might say, "I apologize that I have not gotten back to you yet," or "I apologize that I have not written in so long."
In such sentences, the subjects of the two clauses are the same (The repeated pronoun I). The subjects of the two clauses can also differ, as in "I apologize that the exams are not graded yet, " or "We apologize that you were unable to use your card due to the renewable date." In these examples, grammar obscures the cause of the harm. In the first, the passive clause the exams are not graded yet hides the agent of the non-grading. In the second, were unable (a predicative adjective) and due to (an instrumental preposition) suppress the agency as well. It would be a different message to say "We apologize that we deactivated your card."
The author then provides a solid example uttered by the Republican ex- candidate Mike Huckabee who apologized after he joked that an unexpected offstage noise was Democrat Barack Obama looking to avoid a gunman.
"I made an offhand remark that was in no way intended to offend or disparage Sen. Obama. I apologize that my comments were offensive, that was never my intention.