You misunderstood what they were saying - they weren't being used into a day off, they were being called at the last minutes of short-call, when the next day was a regular, long-call reserve day.

I've been at Delta almost three years, on reserve about half of it, and never been forced to fly on a day off. I don't know anyone else who has either. I guess it could happen, but as Sailingfun said, it's so far down the list of who gets called, it's very unlikely. Basically, there has to be almost no one else on your airplane, anywhere in the company who doesn't want to get paid double-pay to fly your trip.

There are times where a mechanical or other event (think Iceland volcano) forced people into their days off, but that's when there is no other way to get home.

Say there is a 5 day trip that they can't cover - scheduling would break it up into a series of smaller trips in order to cover it, rather than reroute someone into their days off, or force someone to fly on their days off, in order to cover the whole 5 day trip.