Open time is blocked in most statuses for most days. As such, even if no one picked up OT, the company would have no problem covering it via extentions or junior manning. Most pilots have at least 14 days off and many have upwards of 18. That leaves 1-7 days/month the company could cover this flying without returning the lost time off to the affected pilot. Many trips end early in the day, so extentions on short notice would only **** off the typical commuter. Sure, they could call in fatigued, but you can only do that so many times without a problem developing.

Eagle has furloughed 3% of its pilots and even if the pilot group as a whole were successful in not picking up any OT, it would be symbolic only and not bring a single furloughee back faster in this situation, nor show up on the company's financial radar.