In this case, “straight” goes with “truck”, not “driver”. A “straight truck” is a truck that does not articulate in the middle. Compare with a tractor-trailer, where the middle flexes. In the US, a commercial driver’s license that is good for driving a tractor-trailer is also good for driving a straight truck, but the reverse is not true. You can probably imagine what fun it is to back up a tractor-trailer.
In this case, “straight” goes with “truck”, not “driver”. A “straight truck” is a truck that does not articulate in the middle. Compare with a tractor-trailer, where the middle flexes. In the US, a commercial driver’s license that is good for driving a tractor-trailer is also good for driving a straight truck, but the reverse is not true. You can probably imagine what fun it is to back up a tractor-trailer.