LOL, seems the number just keeps increasing every time somebody writes something on these things.
Ich's life cycle in it's cyst form from the time it's dropped from the fish until it ruptures is from 3days -28 days. then it becomes hundreds of free swimming tomites which die within 3 days (peak being 4-8 days) if they don't find a host. that's a total of 31 days ich can go without a fish in the tank to feed on. Or 4 weeks. That is at a tempurature that we keep our reefs at aprox 79 degrees, less temp may promote slightly longer periods beofore the cyst ruptures.
So that's 4 weeks of fishless tank to destroy ich.
most prefer to bump it out to 5 or 6 weeks just to be sure.
12 weeks is a little crazy in my opinion.
The numbers listed above are the works of several marine biologists who are far smarter than me.
http://www.advancedaquarist.com/issues/dec2003/mini2.htm