There is a simpler possibility.
The trace only detects the magic of the caster. The reason that Harry got the note for Dobby's use of magic is because Dobby used inscrutable house elf magic to fake Harry's magical signature.
Or, alternatively, they knew that tracking every spell everywhere there was a child would result in them being inundated with reports, be a violation of privacy, etc., so they have it set to disregard spells cast in known magical areas--basically allowing carte blanche for wizard-raised students, while completely shafting the muggle-raised. That also seems consistent with their policies.
As yet another possibility (and that I was going to use in my HP fic that died with my old comp) the Trace is twofold, both the spell on their wand and the spell on a location, generally their home. This secondary spell is the one that actually detects the magic, while the first merely serves to identify the caster as underaged. Because Dobby would still have to fake something, it would appear to suffer from a complexity penalty, but it would allow for...ah.
I had thought that Riddle had killed his family to create the ring horcrux while he was in school and so should still have the Trace, which research backed up, but which also revealed that he used the wand of the person he was framing for the deeds. Which is rather unhelpful, even if it is obvious. Though he also False Memory-Charmed the man to think that he had committed the deed, which he couldn't use that man's wand for since it was going to be checked, and he was never caught for -that-. That does seem to imply that location is significant.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 90. The previous thread has passed 750 comments.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18,19.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: