2003 Vibe 5 speeds seem to be prone to bearing failures, which 02 corollas didn't, so that makes me think there was a change between the 02 and the 03 trannies
car-part.com is an online tool to search junkyards for parts, and they tie in to some standard interchangeability reference. A search for 02 corolla 5 speed trannies yields nothing newer than 2002, and a search for an 03 Vibe yields nothing older than 2003. I interpret this to mean that the 02 and older are not interchangeable with the 03 and newer.
So, it might be, but if it were me I wouldn't chance it.
The 2002 and 2003 transmissions are likely different in some way.
However, the Corolla 2003 5-speeds don't fail at the same rate as the Vibe/Matrix. I think we determined the transmissions are the same and the heavier Vibe/Matrix 5-speed fails due to the extra weight of the cars.
*Sold* 06' Vibe Base - Mono Platinum - Manual
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Daily 19' Toyota Camry SE Hybrid - Galactic Aqua Mica - eCVT