I see your confusion, however, the authors' claims are utterly without merit. They don't make sense from either of the two most germane perspectives, flavor or health. Let me count the ways:
First, from a flavor perspective, were this the case, the thousands of us who use a lid when grilling would be turning out bitter-tasting food. We're not.
Putting aside a tangential discussion of smoke and acridity, it is flare-ups caused by dripping fats that are more likely to cause bitterness because flames can cause charring and charring often means bitterness. Fats and juices that drip onto lit fuel that sizzle instead of flame are less likely to cause an 'acrid' note to the flavor profile in the short term; over time, dripping foods cooked direct can sometimes take on bitter notes but it depends on a) the food item, b) what the drippings contain other than fats and juices (like marinades), c) proximity to the fuel, d) time.
Use of a lid mitigates or negates the possibility of flare-ups when food is cooked direct. Cooking direct without a lid means either paying careful attention and moving around foods to prevent excessive time in the flames should flare-ups occur; or keeping a water spray bottle handy to dampen flare-ups as they occur.
[Sidebar: BBQ joints that actually barbecue on grills over direct heat are a small minority. But they--like their counterparts, burger joints and steakhouses and open-grill restaurants that grill direct--have someone constantly attending the foods and the grills. Many (in the case of Q joints) cook at some distance above the lit; others (burger and steak joints, open-grill restaurants) cook more closely to the heat but employ movement to various heat zones on the grills to cook their foods effectively and to avoid flare-ups. They are usually cooking many things at once as well so a lid isn't practical. With the attention necessary, nor is it required.]
Second, from a health perspective, there has been much talk of grilled foods being 'bad' to consume. This is because of the PAHs (polycyclic aromatic hydrocarbons), classified by the EPA as cancer-causing agents, that we are exposed to through breathing air contaminated by wild fire or coal, or by eating foods that have been grilled, especially foods that are grilled directly and especially those that are charred. Since charring more readily occurs during flare-ups and since flare-ups more readily occur when foods are grilled directly without a lid, a lid seems prudent at the very least.