I don't see much in a superficial scan of the literature that suggests where the estimate comes from. Someone that really wants to know would want to contact the author for the reference.
If you can see this, you might want to look at an old (1968) paper in JWM
https://www.jstor.org/stable/pdf/3798925.pdf?refreqid=excelsior%3Af02c0884df27abd871237c5de0a992f4
LEAD SHOT INGESTION BY MOURNING DOVES
AND INCIDENCE IN SOIL
JAMES C. LEWIS, Tennessee Game and Fish Commission, Nashville1
EUGENE LEGLER, JR., Tennessee Game and Fish Commission, Nashville
Abstract: Biologists in Tennessee collected 1,949 gizzards from doves harvested on fields managed for public hunting. One percent of the doves had ingested between 1 and 24 lead shot. Pre- and post-hunt soil samples were collected from a field with a history of 8 years of managed public doves hooting. In the top % inch of soil there were 10,890 shot per acre before the September 1 and 2 hunt. The post-hunt sample indicated 43,560 shot per acre in the top 3/8 inch.
More recently (2006) there is this in Biological Conservation
Volume 131, Issue 3, August 2006, Pages 421-432.
A review of lead poisoning from ammunition sources in terrestrial birds
Author links open overlay panelIan J.FisheraDeborah J.PainaVernon G.Thomasb
Show more
https://doi.org/10.1016/j.biocon.2006.02.018Get rights and content
Abstract
Poisoning from lead shot in waterbirds has been well documented globally and, in some countries, legislation exists to combat lead toxicosis at wetlands and/or in waterbirds. However, poisoning of terrestrial species such as raptors and upland game birds, while of potential conservation concern, remains largely to be addressed. For several species, shot are not the only ammunition source of lead, as bullet fragments can be ingested from hunter-killed animal carcasses and gut piles left in the field. This review collates the current knowledge of lead poisoning from ammunition in non-waterbirds. Fifty-nine terrestrial bird species have so far been documented to have ingested lead or suffered lead poisoning from ammunition sources, including nine Globally Threatened or Near Threatened species. We discuss the conservation significance of continued lead use, and detail measures needed to combat lead poisoning.
The 9-15 million thing in the pop-literature article "suggests" to me that they are looking at a statistical estimate with a 95% Confidence interval, but that's just a guess. I have not tracked my way into this article from here.