I don’t know where you saw that, but according to Katya herself in her book “My Sergei” - she lived with her sister, parents and grandparents in a 5 room apartment on the 11th floor of a building on Kalinina Prospekt near the Russian White House. Sergei, his sister and parents lived on the fringes of Moscow in an apartment on the Moscow River - in an area right before it became another town. So she and Sergei were never next door neighbors. They attended the same sports school - CSKA - and she began attending it when she was 4, but Sergei would have been 8 or 9 and if I remember correctly - older skaters had their own rink or available ice times.