Yes, some might disagree because they know the facts surrounding your urban legend. Especially those who were involved with pilot hiring and quite familiar with the EEOC case at UAL. BTW, this topic seems to surface every year or so and has been discussed over and over. Doing a simple search would provide ample background.

What you want to search for is the EEOC consent decree. While UAL was named in the decree, all carriers complied at the time. There was some preferential hiring following the decree (early to mid 80's) until the carriers showed that the decree could not be complied with based on demographics. In other words, the EEOC required number of minority and women applicants with pilot ratings simply did not exist.

As for tribal affiliation; Contact the tribe and ask what the procedure is for obtaining a CIB card (Certificate of Indian Blood). Once you hold a CIB card, you can apply to become a member of the tribe. Until you've completed both steps it would be foolish to make the claim of Indian heritage on an employment application.