Innerstin stuff Fred. Why do I have this uneasy feeling that things are not exactly as they appear???
Try a little 'kitchen-physics' - uplift is due to magma - and as it cooled, just as a cake baked in the oven does, it sinks in the centre:
It's known as the Taklimakan Desert. Looks like a lakebed to me...
The Altiplano, filled with water: Elevation 15,000 feet.
The suggestion that Lake Titicaca was lifted to its present elevation of 12,500 feet through some unspecified catastrophy was made by Velikovsky in "Earth in Upheaval" (1955). The archaeological record would have suggested that this would have happened in historic time, after Tiahuanaco was already built. But the archaeology of this site (built after 800 BC), the conditions of local agriculture (abondened terraces at the snow line, sterile conditions, "maize will not ripen"), or geological details (raised beaches, slanted strand lines, marine crustacians), cannot sustain this. It seems more reasonable to suggest that the Alto Plano and the Andes mountains were raised maybe 3000 or 4000 feet by the intrusion of magna below the established Cordilleras
What is more convincing is the occupation of the site at about 1400 BC and and a thorough exploitation of the available agricultural conditions...
Warning, graphics-heavy:
If you Google Earth Lake Titicaca, you will find huge areas of agricultural activities - now underwater: