An area that's been badly burned is very sensitive and easily damaged. Until a solid base of vegetation is reestablished, any tracks at all can lead to the establishment of erosion patterns that become difficult and expensive to correct. That's especially true in desert or high mountain areas where the vegetation doesn't have the easiest life to start with.
Here in Utah, there's no question that a badly burned area will be closed to motorized traffic while it recovers. There in Oregon and Washington, it's wet and temperate enough that maybe that doesn't happen nearly as often? In the Rubicons case I would expect it to depend on the fire behavior. If a fire crawls through the area and just burns a little undergrowth the way a fire in a healthy forest does, no harm no foul. But a fire the size of this one with the lack of containment this one has isn't burning in a healthy forest. This one is up and running, feasting on the fuels left by decades of fire suppression, and it's likely burning everything to the ground. If it hits the Rubicon while it's acting like that, the area will be devastated, and I'd expect them to close it on general principles.
