That's the implication of her argument, you're right. But she doesn't even claim to make an argument - she denies it, in fact, by affirming a "perceived personal burden." That, in turn, has to be itself implied as referring to religious belief protected by the 1st Amendment. And then underneath it all is her fundamental implication that the government is superior to the people in all cases, and that that position is in fact the very purpose of government itself.
So much for "We the People."
I've read a lot of twisted legal arguments. I can confidently say, however, that her "question" is THE most twisted legal "argument" I've ever read. And because it's from a USSC Justice, it's all the more shocking.
America is in a LOT of trouble.
Even fairly sophisticated commentators seem not to realize the damaging legal theory that is taught and practiced as a monopoly in law schools and the legal system.
Sotomayor, Kagan, and Ginsberg have no business as Justices.
Sotomayor shouldn’t even be a judge.