The wedding could go down in a book of wedding disasters--an outdoor wedding and reception hit by a sudden deluge driving everyone and everything inside. Tim does not change it, because Mary (who does not know that it could be changed) says she would not change anything about it. She also does not know that one thing has been changed, and changed several times. Rory was originally chosen to be the Best Man, but his toast was a disaster, so Tim went back and picked Harry instead, whose toast was offensive, so he goes back again and chooses Jay, whose toast is even more offensive. In the end, Tim's father serves as Best Man, and offers a heartfelt toast, three trips to the past to get someone in the spot who far from ruining the event will make it truly memorable.
Yet this time it is Tim's Dad who is unhappy with his own toast, so he goes back from later in the reception to redo it. Tim asks him not to change anything, but he changes it anyway, and says some wonderful words about the men he has loved which were an excellent part of the script, and the more so by the suggestion that they were what he decided he should have said, and so he went back and said them.
How, though, does Tim know this?
Tim is the narrator; he tells the story from his own experience. We understand that when he travels to the past, he remembers the events of the history before he changed it, and any events he experiences while he is in the past including the entire altered history if he does not then skip back to the future. He has no memories of events in the altered history if he skips them, but he is aware that they are changed due to his intervention. However, ordinarily when his father travels to the past Tim is not aware of the event, nor of the erased version of history. Why, this time, would he remember his father's original speech as well as the altered one?
Of course, this time his father discusses his intention to change the speech before he does it--but how would that matter? We have an original history in which Dad makes the speech, then in the aftermath tells Tim what he should have said, and that he is going to fix it because he can. Dad travels back to the dinner, makes the revised speech, and whether he lets the clock run or jumps to the future, in the aftermath his doppelganger in the new history will have nothing to say about revising the speech--it has already been revised. Thus the only history Tim remembers includes the revised speech and does not include any suggestion by his father of making that revision.
Certainly under the rules of time which seem, loosely, to apply in this film, that is a perfectly possible version of events. What it is not is a version of events which could be known by the viewpoint character who tells the story of what happened in his life. The film has in that sense broken its own rules--not its time travel rules, but its literary rules.