You can only patch games that are Live enabled. Halo is Live Enabled, TSL is NOT Live enabled therefore you can NOT patch TSL on Xbox.
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And regardless, MS doesn't allow bug fix patches as such, period. Ever. They allow downloadable content. So even if TSL were a Live game, which it isn't, MS would not allow a bug-fix patch.
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What about Unreal Championship? Im sure it had a few patches with Bug Fixes.