You will be glad to know that you are indeed right!!!
Lake Titicaca is the highest commercially navigable lake in the world, at 3,812 m (12,507 feet) above sea level. Located in the Altiplano high in the Andes on the border of Peru and Bolivia, at 16°S 69°W, Titicaca has an average depth of 107 m, and a maximum depth of 281 m. The western part of the lake belongs to the Puno Region of Peru, and the eastern side is located in the Bolivian La Paz Department.
More than 25 rivers empty into Titicaca, and the lake has 41 islands, some of which are densely populated.
Titicaca is fed by rainfall and meltwater from glaciers on the sierras that abut the Altiplano. It is drained by the Desaguadero River, which flows south through Bolivia to Lake Poopó. This accounts for less than five percent of the lake's water loss, however, the rest is caused by evaporation as a result of the strong winds and sunlight at this altitude
Hope this helps!