Unfortunately, given the times, I am supposing your question is asked in bad faith. But if "society itself viewed her as black" and then society itself found out that she was systematically lying about her childhood[1] and past experiences of discrimination[2], then society can certainly change its mind.
The real thing about race being a social construct is better expressed by Dubois: "the black man is a person who must ride Jim Crow in Georgia." That is, you can't discuss race without understanding that it's nothing more than a psuedoscience designed to enforce a hereditary and geopolitical caste system - discussing it taxonomically is a sucker's game.
So while Krug might have been able to successfully lie about being black (while also styling her hair/makeup to make the ancestry more plausible), that doesn't mean very much when she actually spent her life at the front of the bus.
EDIT: On race being "oppression first, ancestry later," see also former NAACP leader Walter Francis White, whose recent ancestors were mostly European but whose parents were both "clearly" black. White himself was blonde and had blue eyes, and he often went undercover as a white man. From Wikipedia[3, racist slur censored for HN friendliness]:
> Granted press credentials from the Chicago Daily News, White gained an interview with Arkansas Governor Charles Hillman Brough, who would not have met with him as the NAACP representative. Brough gave White a letter of recommendation to help him meet people and his autographed photograph.
> Learning that his identity was discovered, White was in Phillips County briefly before taking the first train back to Little Rock. The conductor told him that he was leaving "just when the fun is going to start" because they had found out that there was a "damned yellow nr down here passing for white and the boys are going to get him." Asked what they would do to him, the conductor told White, "When they get through with him he won't pass for white no more!" "High yellow" was a term used at the time to refer to black people of mixed-racial descent and visible European features.
[1] https://twitter.com/GrahamStarr/status/1301567380313829381
[2] https://twitter.com/JedMSP/status/1301570822545391616
[3] https://en.wikipedia.org/wiki/Walter_Francis_White