The 1/32 rule allows real Indians who are 100% Indian to belong to some recognized tribe. Else, you could find some of those recognized bands dwindling down to a handful of people.
Remember, it's not how Indian you are, but what's your blood quanta running back to someone who was listed in the Dawes Rolls.
Thanks for that explanation. Around here the tribes tend not to mix quite so much, and most are from one band or another.