Hydraulic elevators had just been invented and the passenger elevators in Virginia City and San Francisco were among the first in the country. Pre-hydraulic passenger elevators had been invented by 1857 and the Otis Elevator Company installed their first one in a store in New York City in the same year. By 1875, according to the Otis Elevator Company Historic Archives in Farmington, Connecticut, the company had installed passenger and freight elevators throughout the United States including in New Orleans, St. Louis, and at the Occidental Hotel in San Francisco. In addition, the Otis Company was not the only elevator manufacturer in the country at the time. Anyway, it never hurts to ask how do they know and can they prove it.
People can say anything, and generally do.