To me, "Carrier has my back" is a misleading and dangerous assumption for an owner-operator to have.
As a self-employed professional who brings one's own capital to the game, the best approach is that of a self-employed professional. Expediters who rely on their carrier or anyone else to have one's back, take care of the contractor or get the contractor where the contractor wants to be does so at his or her peril.
Think about it, will a carrier come to your aid if money is short and a major truck repair is needed? Will a carrier pick up your medical bills if you fall ill or become injured on a run? If you receive word that a serious issue developed with your house, will your carrier assist by sending a repair person so you can stay out and remain productive? If your truck is spray painted with graffitti, will your carrier pick up the cost of a new paint job? If you leave, how many minutes will it take for a carrier to replace you and continue its operations? When a carrier is contemplating a business or policy change, how much time do the decision makers think about you by name and consider the impact such changes will have? When you die, will your carrier send a representative to attend your funeral or provide a gift to help out your family?
In general, carriers do not think about you. They think about their fleet, the fleet's ability to serve the carrier's customers and the expense of maintaining the fleet.
That said, some carriers are better than others at showing compassion and understanding a contractor's circumstances. Some are better than others at keeping their word. Some are better than others at setting and maintaining high safety and truck maintenance standards. Some are better than others at teaming up with the contractor to provide exceptional customer service while making sure the owner-operator's needs are met at the same time (detention time, extra pay for work or miles added after a load is dispatched, etc.). But none of this should be mistaken for "Carrier has my back."
In business, the only person a business owner can count on for having one's back is one's self. Your health, safety, prosperity and well being are yours alone to maintain.