The paper's authors implied that, because of the cool but arid climate, fires in the savannas of paleolithic North America were less frequent than they are today. I was basically relaying the author's statement but I suspect the key here is the intensity of the fires, more than the frequency. Wooded forestlands have a tendency to collect more high grade fuel over time so, when a fire does break out, the result can be a major conflagration.

Bear in mind, the savannas of 14,000 BC were not the same as the prairie found in the Midwest today. Because of the changing climate these savannas gave way to a mixed tree-grass forest ecosystem. Although fire is thought to have played an important role historically in the dynamics of many mixed tree-grass vegetation systems, the details are poorly understood, especially for oak savannas in central North America prior to European settlement.

Wildfire occurs naturally and plays varying roles in nearly all terrestrial ecosystems. Because different types of ecosystems produce and accumulate fuel more quickly than others, the frequency and intensity of such fires are determined by the type and the stage of development of the ecosystem in which it occurs. Most North American terrestrial ecosystems were/are dependent to some extent upon fire and many plants have evolved adaptations that protect them from wildfire.

Today, fires in the prairie usually occurred in five- to ten-year cycles, with moderate regularity. Fire in tall grass prairies acts to burn above-ground biomass, killing woody plants, allowing sunlight to reach the soil, and changing the soil pH and nutrient availability. Grassland fires can cover large areas in a short time as fire fronts are driven by prairie winds. However, because grass provides a low quality of fuel, grassland fires usually are not intense. Because of predominantly westerly winds across American prairies, trees are sometimes found on the eastern bank of streams and rivers that stop fires spread by these winds.

As for fire in modern forests, it depends on the region. For example, Southern pine forests, consisting mainly of loblolly, shortleaf, or longleaf pines are found from Texas east to Florida, and north to Maryland. Lightning ignited fires in southern pine communities are common. More frequent fires favor longleaf pines, which are more fire adapted; less frequent fires tend to favor shortleaf and loblolly pines. Frequent fires also create pine savannas when shrubs are burned away, favoring the establishment of grasses beneath the pines.

Some references: Fire Dependent Ecosystems of the United States, and Effects of Fire Frequency.