This is an exaggeration; Brinkley had not claimed anything like 10,000 procedures at this time (or at any point in his career). He was quoted in 1923 as having done 3,000; in 1926, newspapers reported 4,000; and in 1938, the AMA estimated the total number as between 5,000 and 6,000.
References
Brinkley claims "more than 3,000 operations performed" ("Gland Transplantations Now Used By Japan To Put Aged Infirm Back To Work, High Class Goat Prices Soar," Springfield Missouri Republican, 16 Mar 1923, Page 10); "between 5,000 and 6,000 persons" ("The Case of Brinkley v. Fishbein", Journal of the American Medical Association, May 13, 1939, Volume 112, No. 19, p. 1958); "Preaches Fundamentalism Practices Goat Gland Science," The Times Recorder, 7 Nov 1926, Sun, Page 24.