Can someone skip being referred for a liver transplant all together?

There is a lot that goes into transplant compatibility. Is this person donating a portion of their liver?
Talk to your doctor. They may not even be a viable portion donor.
Either that, or just perform the transplant in your garage but just remember to sterilize your box cutter for the incision.

You may not be put on a waiting list, but that is assuming the donor is compatible. There is a ton of legality and liability when it comes to transplants. They won’t “skip” anythig.