"I apologize for any inconvenience." That is, "I regret (out of prudence rather than contrition) if your excessive sensitivity falsely found fault with my innocent actions."
False Apologies
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Mr. Stanley’s Aphorisms and Paradoxes are outstanding examples of the long-form aphorism... inevitably studded with discrete individual aphorisms that could easily stand on their own.
-James Geary, author of The World in a Phrase: A Brief History of the Aphorism