Actually, to be specific, there is no legal "sponsor" of a visa. There is a "petitioner", the person or entity who seeks the visa. B visas are self-petitioned, others (such as K, H, L and others) are petitioned by an external party and cannot be self-petitioned.
I think this is where the confusion comes from, and it's also worth noting that while likelihood of a public charge is a grounds of inadmissibility, an affidavit of support isn't the only way to get around it. I didn't need one for my GC (although my wife did). Additionally, the requirements to execute an affidavit of support are MUCH looser than those to petition for a visa.