Yep, Derg is right. What you're talking about deals with offline jumpseating. Using another airline's jumpseat for your company's business, saving your company money, is a big no-no. But riding your own company's jumpseat while on a deadhead isn't a big deal, provided that you don't bump a jumpseater in the process.
That was delineated pretty clearly at Skyway.
They even said, "If you're flying to work, you are NOT, you are just flying because you're working in a couple days. If crew scheduling tells you to ride the jumpseat, refuse to else we'll lose the benefit".
That stuck with me.
But I will never in a billion years say, "If I don't make this flight, I won't make it to work" otherwise it just indicated a lack of planning on my behalf.