The risks of exposure to lead are most certainly not overblown. Lead is among the most studied environmental contaminants, and we know a great deal about exposure pathways and the effect of lead on the human body. Any shooter who chooses to believe otherwise, almost certainly doing so with total ignorance of the extensive body of scientific literature on lead toxicity, is deluding themselves and potentially compromising their own health and that of their families due to lead contamination brought home from the range on clothing and shoes. Young children are particularly sensitive to lead because their nervous systems are still developing, and numerous studies have shown reduced IQ scores due to lead contamination.
So, there is absolutely no question that lead in the body can lead to a variety of health problems; the only remaining question is whether our shooting hobby can result in concentrations sufficiently high to be of concern, and unfortunately the evidence is overwhelming that it can. The primary route of lead exposure for most shooters is inhalation of particulate lead, derived both from lead bullets and lead styphnate priming compound, in indoor ranges, although there are indications that exposure at outdoor ranges may also be problematical. (As an aside, arguments I've seen that lead is "too heavy" to be suspended in air are nonsensical and show a total lack of understanding of the settling behavior of very small particles in a fluid.) Just about all (100%) of inhaled lead passes into the bloodstream through the lining of the lungs. A secondary route of exposure is ingestion of lead, usually as a result of eating after handling lead without first washing the hands. Although the studies I've reviewed have reached somewhat different conclusions, it looks like 40% or so of ingested lead enters the body. Elemental lead does not pass through the skin, so handling lead during reloading (for example) is not a problem, except as it may result in ingestion. I have not been able to find any information in the scientific literature regarding whether lead that may become dissolved in common gun cleaning solvents will pass through the skin, but prudent shooters will assume that it can and take appropriate precautions.
The route by which the lead enters the body doesn't affect its toxicity - what's important is the body burden as measured in the blood (serum). The current guidelines issued by CDC are less than 10 mcg/dl (micrograms per deciliter) for adults, and half that for children. I wouldn't be surprised if those numbers are lowered in the future based on additional research. Shooters should ask their doctor to add lead as an analyte to the blood test done for their routine physicals and, if these concentrations are exceeded, take steps to identify exposure routes and ways to reduce exposure. As an example, I was able to reduce my serum lead concentration from about 31 mcg/dl to 7 mcg/dl in about two years by wearing a respirator when shooting indoors.
Because the OP asked for input from scientists, I'll just briefly summarize my background: Over 40 years experience as an environmental scientist working in (among other technical disciplines) hazardous waste site remediation, environmental toxicology, and human health risk assessment. With a couple of partners, I own an environmental consulting/engineering company and serve/have served as a consultant to EPA, several other Federal and state agencies, and numerous corporations.