I'm not aware of a tribe that requires 100% bloodline, typical standard seems to be around 1/8 to 1/16. There is actually a pretty high bar to get membership in most tribes, and this treaty is not with all tribes just this particular tribe.
Anyone can take a blood test and say I'm x/x native american, but joining a tribe (especially those with some sort of benefits, mineral royalties, casino income, etc.) can be extremely difficult. Typically to gain membership you have prove lineage, for instance to become a member of the Cherokee tribe you have have someone in your direct lineage that was on the tribal roll (Dawes roll), this means you have to furnish the tribe with birth and death certificates for every relative back to the individual on the role, some tribes like the crow require that if your grandparents weren't married that you provide blood tests... which is impossible if they are deceased. If your bloodline is to your father, grandfather, etc. and they aren't on the relevant birth certificate than your sol... also as I referred to before if an ancestor was born before 1952, and was adopted off the rez then those records are likely sealed, and a new birth certificate issued. It was also common practice to change the race of babies on birth certificates. It's very possible to take a DNA test have it show > 50% native american heritage and not be able to gain tribal membership... saw this play out first hand.