I'll offer this caution, but unfortunately I don't have a direct answer to your question.
Many times companies will have a position on what is OK; typically they are correct and offer safe products. But there are exceptions and DEX VI is one of them.
GM fully states that DEX VI is backwards compatible in all their applications. However, the Allison 1000 series transmission, up until mid-2006, had seals in it that were not compatible in the long term with the chemistry package of DEX VI. Allison specifically forbade the use of DEX VI, until seals were changed over, and they still to this day to not reccommend DEX VI before a series of serial number cut-off units for both the INDY and Baltimore made trannies. So, what you have is the maker of the trannies telling you that DEX VI is not backwards compatible, but GM telling you it is. For a while, GM owned Allison, and so they "bullied" Allison into a postion of accepting DEX VI for a short time. Allison did change over seals in mid-2006. The Allision 1000 series tranny is still made at the Allison-owned Indy plant, and also the GM-owned Baltimore plate. When GM sold off Allison, they kept the rights to manufacture and use the Allison name on that one tranny. So, you see, this is very much a topic of "it depends" ... on your point of view. But CLEARLY are applications to this day where DEX VI is not a good choice for some trannies.
So how does this apply to you? Neither you nor I have any idea if the DEX VI will react badly with the seals in your 2002 tranny. It may be safe, it may not. And I doubt you'd ever get a good answer specific to this topic from either GM (they will stick to the full company line of it being OK) or Toyota (who will probably tell you to buy their fluid). The seals, if they react with DEX VI, will not go bad overnight, they will degrade over time. You'll start to get leaking around the seals as they deteriorate, etc. This might apply to both internal or external seals. I cannot assure this will happen; rather this is a cautionary remark about what might happen, as we don't know what kind of seal materials might react with the DEX VI chemistry.
You have a few OK options in my opinion:
1) any DEX/Merc type fluid is probably going to be OK - most of the reputable companies still make these the same way they used to, and so if they were good enough to be reccommended back in 2002, they are probably still OK today
2) use an Allison TES-389 approved fluid - that spec was specifically generated after GM stopped licensing DEX III, and it is essentially a clone spec for the DEX III fluids, with the added assurence of seal compatibility! You can find a list of those approved fluids at their site
Caveat Emptor.