I admit that 26 year old tyres still in service is extreme. However, that does not change the analysis that is needed to determine if a tyre (of any age) is acceptable for service.
The original poster implied by his question that a 6 year old tyre may not be acceptable as "new". Indeed, it may not be acceptable, if the tyre was not stored properly. On the other hand, as I mentioned before, age alone is not the determinant of acceptable serviceability.
As for my own deep thoughts on my own tyres ages.....I'll ride the 1982 Michelin's....as they grip as rubber should (like street compounds did from the late 1970's and 1980's, not like silicone compounds of the 1990's), they have been stored away from UV sources (so there is no cracking or micro cracking), they are undamaged (no tears, cuts, gouges, etc), they are unworn (lots of tread).
I would encourage @Canada, the original poster, to examine his 2002 tyres in the same way. And, depending on how quickly and how much wear those tyres are going to get - tyre age may not be an issue at all.