harry potter - Why Did Dudley Have to Have His Piggy Tail Surgically Removed?

Why did Dudley have to have his piggy tail surgically removed? Why wasn't the Accidental Magic Reversal Squad dispatched to remove the tail and modify the Dursleys' memories?

After Uncle Vernon insults Dumbledore one too many a time, Hagrid retaliates by giving Dudley a piggy tail:

He brought the umbrella swishing down through the air to point at Dudley – there was a flash of violet light, a sound like a firecracker, a sharp squeal and next second, Dudley was dancing on the spot with his hands clasped over his fat bottom, howling in pain. When he turned his back on them, Harry saw a curly pig’s tail poking through a hole in his trousers.

[...]

‘Shouldn’ta lost me temper,’ [Hagrid] said ruefully, ‘but it didn’t work anyway. Meant ter turn him into a pig, but I suppose he was so much like a pig anyway there wasn’t much left ter do.’

_{Philosopher's Stone - page 48 - Bloomsbury - chapter 4, The Keeper of the Keys}

So Hagrid's magic didn't work right. Dudley subsequently has to have the pig's tail surgically removed in a Muggle hospital:

‘All right, we’ll take you to King’s Cross. We’re going up to London tomorrow anyway, or I wouldn’t bother.’

‘Why are you going to London?’ Harry asked, trying to keep things friendly.

‘Taking Dudley to hospital,’ growled Uncle Vernon. ‘Got to have that ruddy tail removed before he goes to Smeltings.’

_{Philosopher's Stone - page 68 - Bloomsbury - chapter 6, The Journey from Platform Nine and Three-Quarters}

First, Hagrid is barred from using magic at all. Second, to knowingly use magic in a Muggle-inhabited area, or in front of a Muggle, violates section 13 of the International Confederation of Warlocks’ Statute of Secrecy (OotP - chapter 8, The Hearing). Third, when Harry produces a Patronus in front of Dudley during the Dementor attack in Order of the Phoenix, he immediately receives a letter from Mafalda Hopkirk advising him that he has been expelled from Hogwarts and that he will need to appear for a disciplinary hearing at the Ministry.

How did Hagrid get away with using magic in front of Muggles, and not have been brought up on charges of breeching the International Statute of Secrecy? Since he meant to turn Dudley into a pig, but only managed a piggy tail, does that constitute "accidental" magic? Why didn't the Accidental Magic Reversal Squad show up, magically remove Dudley's tail and modify all three of the Dursleys' memories like they did when Harry accidentally inflated Aunt Marge¹?

★ I do not prefer any answers from the HP Wikia or the Wikipedia.

¹_{Technically, Aunt Marge was the only Dursley to have her memory modified. The Accidental Magic Reversal Squad left Vernon, Petunia, and Dudley alone.}

Answer

Hagrid was old enough that he no longer had "the trace" on him so the Ministry no longer could monitor his magic activity. Initially I thought "but what about Harry's trace?" but Harry hadn't started school yet and I seem to recall that due to that he didn't have the trace put on him yet.

So the answer simply seems to be that the ministry never knew that Dudley had a tail magic'd onto him and Hagrid didn't seem to feel the need to inform them.