If you actually "take full and personal responsibility" for something, you say so and stop talking. Hillary Clinton says that she takes "full and personal responsibility" for losing the presidential election last year, and then goes on to say that she also lost because of James Comey, Russian interference in the election and self hating women who would not vote for her. In other words, she takes no real responsibility at all.
There is, however nothing unusual in that, this is the way modern politics works. "I apologize if anyone took offense."