That was very common in those days.
My barber, who shaved lots of men in the 60's and 70's with straight razors also told me that the wealthier customers had their own straight razors stored in the barber shop. Also, it was common that those wealthy customers booked shavings in their own houses. My barber told me that there were some rich customers that paid my barber to have him go to their house and shave them with their own straight razors.