The guy was flying west against the jetstream, so the published capability would be even less.
Since it was a delivery, they usually put extra fuel on-board for trips like this.
It sounds as if they miscalculated the headwind.
Worked on a C-310, years ago, that was going to HI. They had removed the rear 4 seats and installed a cradle that held 2 55 gallon drums on bottom, a 30 gallon drum on top. The pilot also had several 5 gallon cans on the co-pilot floor so he could add that if needed. This almost doubled the original fuel capacity. Common method of getting planes to HI.
As others have pointed out, it is usual to add auxiliary fuel tanks for flights like this, putting the range well above the published maximum. Permission is required from the FAA for this since it also puts the gross weight above the rated maximum. The FAA evaluates the proposed modification and either issues or denies a waiver on that basis. Most light planes will lift a very substantial overload since rated maximum gross weight is based on what is safe for routine, day-to-day operation and not the maximum that could be handled on a one time basis.