IE, the issue isn't that drivers transport fuel, but that possibly tired drivers do so.
Nobody in trucking gripes about limited working hours. The current hours per week available for work are more than enough to work at an unsustainable rate of sleep. What everyone bitches about is the electronic logging requirements that prevent them from cooking the books in order to account for delays that happen over the normal course of business. Because people can no longer cook the books they do other things that increase risk.
For political and optical reasons the DOT can't exempt them from e-logs to make their lives easier. So they just exempt them from all of it. They're basically saying "if you're gonna push yourselves we'd rather you cut the smart corner and work a 12hr day than drive around like maniacs trying to fit X hours of driving in a Y hour window."
Normally the pipeline would pump huge amounts of fuel around to various distribution centers where trucks and tankers would then haul it the last leg to e.g. gas stations and other end users. Now there will be far fewer distribution centers to pick up the load from, and much longer distances to drive to deliver the product.
Naturally a pipeline has much greater capacity than a string of trucks, not to mention the impacts on traffic and safety concerns that go with pushing the truck drivers that far. The limited number of distribution points with the pipeline offline will probably have a logistical impact as well since there will be an imbalance re: how many trucks are arriving to get filled up.