While I can't provide a legal opinion due to the terms off the website and the requirement to review each and every detail of the event I can provide some general information related to liability. It is true that a vehicle pulling out into traffic generally does not have the right of way and will generally be deemed as the at fault driver. With that said his liability is not absolute. By that I mean that if the moving vehicle (Traveler's) is speeding, changing lanes such that had he not changed lanes he would not have hit your friend and or negligently looking down not forward. These are all factors that could show that the negligence of (Travelers) was the proximate cause of the accident. You also mention that other car's had yielded to allow him to enter traffic. This again is another factor that could lead to a showing that (Travelers) negligence was the actual cause of the accident. Since you mention the driver did not have insurance yet it would be highly recommended that he contact an attorney immediately for a consultation. Most attorney's will provide a free 30 minute consultation to review the facts of the case along with potential legal claims.
Since this is a company vehicle it is more likely that an attorney will take the case and also that Travelers will pay versus just suing the average person that does not have insurance as an example. It is highly unlikely that anything done by the driver will not change the decision by the insurance company. It will likely take direct contact by an attorney and may require him to file suit before they will consider a different response. This is just based on my past experience in dealing with any insurance company.
I am sorry as this usually also means that there will be some time between making demand and actually getting payment. A local attorney could lay out those timelines better, but unfortunately its is not a quick process as it would be if the insurance just agreed to pay.
I don't know the costs involved, but most companies of this size self insure and by that I mean that for the first 1 Million dollars the company pays and then they probably have coverage that kicks in after reaching that amount. I say this just so you know that the company may ultimately be the one making the decision to settle the case. Most times this is better than having the insurance company decide everything as they would for you or I on most personal vehicle insurance. He will never know how the insurance is covered by the company until he files suit and his attorney makes a demand for records, etc as part of the lawsuit.
I am sorry that there is not a quick quote or him citing some case law that would make a difference. At this point I believe he needs to retain an attorney first to fully understand his rights and then if it makes sense then the attorney will know the best process for moving things forward.
Again I am sure this is not the answer you were wanting, but I have an obligation to provide the most accurate information to you as I can and though not an official legal opinion I am basing this answer on my past interaction with insurance companies. Typically I only spoke to clients like driver where the insurance failed to respond and basically they had given up and consulted wiith me and ended up with a settlement. Note I did not typically deal with auto wrecks as that is usually the personal injury guys on TV, but it is very similar for homeowners & commercial policies.
I wish you/him the best and do remember that even after rating my answer you are welcome to reply with additional questions related to your original question for free as long as needed.