Answer
No, distance from the center alone does not determine safety. Montevideo has quiet central neighborhoods and outlying areas with varying infrastructure and risk levels. An empty street, infrequent public transport, and poor lighting may be less convenient, even if the area is far from the tourist center.
Assess the specific address: official statistics, the level of street activity during the day and in the evening, the route from the bus stop, the condition of the building entrance, and feedback from several local residents. One neighbor or rental agent does not provide a complete picture.
For everyday life, balance is important. A very quiet area may require a car and long trips, while a busy area may require vigilance against pickpocketing. Visit the area at different times and check your usual routes to work, school, and shops before signing a lease.