The question of the owners themselves is a separate matter which is what those who agree with Obama keep trying to pretend makes the whole issue go away. It doesn't. Defining a special class of persons based on the desires of the government to limit rights in one instance will always lead to defining more classes the government wants to deprive of specific rights due to the "common good" being more important than the individual.
The court could stipulate that the corporation is a different sort of person as a way to hide the fact that they are taking away an individuals rights by creating such a definition, but if they do they destroy the definition of a person to some degree.
They've already sidestepped the issue of differing classes of persons on numerous occasions by avoiding cases that would define a conceived child as a person at some point which is why folks think they may try to sidestep the issue again. Obviously those arguing for the government believe they have the right to create classes of persons without some or all of the rights the Constitution guarantees whenever they see fit to do so.
Keegan made herself look like a complete idiot trying to focus on what's a burden rather than the real issue but making herself look like an idiot probably isn't unfamiliar and therefore uncomfortable territory for her.
This already exists — just look at ex-felons (that is, those having served their entire sentence) and how they are denied arms, voting, and serving on a jury.