Forget society, she's doing a service to ME. Why? Because if all else failed and her grandmother were dying in the street in front of me, I would feel a moral, ethical, and emotional obligation to assume her care. I would rather pay in to BI, if that worked to remove this scenario from possible things that might happen. That's my personal felling about it, without parsing all the possible socioeconomic ramifications.
But why should your personal moral dilemma define legislation for all citizens across the country? I have an issue with "it makes ME feel bad, therefore make it law." You can use the same basic argument against gay marriage.
Regardless, the grandma won't be doing in the street without BI, just like she isn't now. I'm not arguing against providing care for the elderly. I'm just saying that if a single individual chooses to spend her life caring for another single individual, maybe that person isn't performing a service to society. Maybe she's performing a service to her grandma, and nobody else.
And hence "society". Social costs and benefits (also known as "externalities") are simply costs and benefits to anyone outside of the decision to engage in a excahnge.