After some more thought, this is what I think about these fuses: at the circuit level, they adjust the effective transistor area, nothing more, nothing less. It makes sense perfect for the steps to be binary - wide trim range and fine steps with a small number of fuses. As a sidenote, Vishay foil resistors use a similar approach to trimming.
The low-level transistor equations feature current density rather than current, so essentially doubling a transistor's area is the same as halving its collector current. So in the classic refamp designs you always see the SZA and current-setting resistor listed as a matched set in the parts list - the resistor is hand-selected for a certain zero-TC current. With the newer LTFLU, the part can be trimmed at the factory and a constant current can be used, and more importantly a constant resistor value - a huge plus for manufacturability. The trimming is almost surely done on an ATE-type system at the wafer level, before dicing and packaging, and most probably at room temperature, probably based on voltage measurements at constant current. In support of this theory, please see the LT1236 teardown on this forum. It has fuse trim pads that are used for coarse trim before packaging, as well as bonded-out trim pins labeled Do Not Connect, used for post-packaging fine trim.
This is how I see it at least, only Fluke and LT\AD really know the details...