In your case, you're the only employee of your business. And if you're not there the business will literally go under. And you also get directly rewarded for being there. I would guess that being 'on call' in this manner is possibly less draining on a person's soul (depending on how well they tolerate the risk of owning a business).
Contrast that with being 'on call' for your megacorporation, who isn't giving you anything extra for your on call time because they 'already pay you enough'. And where the only negative consequence for the company if you fail to immediately respond within 15 minutes is that some executive in the company is kept waiting longer than 15 minutes, or some ads aren't being shown for 15 minutes.
But if you aren't there, your boss is going to get a phone call and that's definitely not going to look good on you. And there's no bonus for fixing the problem, that was already your job in the first place. Sucks that you had to do it outside of scheduled hours, oh well.
I'm with the author of this article. Take your on-call rotation and shove it (if you're a large corporation). I'm fortunate enough to be able to take a firm stance on this point, and do so happily.