I was on the part 135 side of the house. I don't know how it plays out for the 121 supplemental, but as per an FAA LOI (letter of interpretation) to a Mr. Hernan E. Orellana (and also in a few other LOIs that were distributed throughout the past decade) dated October 6th, 2015: the "rolling rest" policy that IFL (and every other part 135 carrier in that industry) uses is completely, and indisputably, NOT allowed under the requirements of 14 CFR 135.267.
Approximately two days after this LOI was released, I emailed it to the chief pilot on the 135 side, and CCed it to the Director of Operations for IFL. The response I got back from the CP was, "Interesting." That's it. I followed up when I made it back to PTK and walked a print out of the letter into the CPs office. He shrugged his shoulders and said, "Yeah, but if we follow that then we can't stay in business. You can talk to the DO if you want." So, I walked across the hall to the DOs office and laid the letter on his desk and asked, "How does IFL plan to adjust their operations in order to conform to this Letter of Interpretation?" Without looking at the letter, he stared me straight in the eye and said, "We aren't doing anything wrong." Rather than allowing him to try to pressure me into dropping the subject, I played the staring game that MC (the director of operations) is so good at. After we stared at each other for over a minute, he tried to threaten me by saying, "Well, if you need to know exactly when your duty day is maybe we need to start having you show up to the office for 14 hours a day to sweep floors." I responded, "How you implement the LOI is up to you, but it's implications are clear." He stared at me some more and finally said, "I actually haven't read the letter yet." So, I said, "Mr. C***, how can you presume to tell me that we aren't doing anything wrong if you haven't even analyzed a new LOI that the FAA has just released?" He told me that he would read the letter and get back to me. A few days later, I got an email from him that said, "We're not doing anything wrong. Talk to our lawyer."
So, I then emailed the company's chief counsel. The reply that I got was that IFL "Completely agrees" with the contents of the LOI and that "that is why IFL does not at any point require any of it's pilots to answer the phone if they don't want to, and no pilot has ever been reprimanded for not answering a call."
I replied to the Chief Counsel that I appreciated his response and asked him how he explained the fact that, literally within the past two weeks, IFL had just fired an FO on the Falcon because he hadn't answered his phone when he was called for a trip.
I never received any reply.
After raising this issue with the Chief Pilot, Director of Operations, and Chief Counsel, I was subsequently assigned to be based at an out-station (TVF) for 4-5 months, with no option to say "no", so that I would stop "causing trouble" in PTK.