While it is true that TMT could be located at another site, no site would be quite as good as Mauna Kea.
Astronomers measure the quality of a site in several ways, one of the most important is simply called ‘seeing’. This is a measure of atmospheric distortion, the amount of turbulence in the atmosphere above the telescope that distorts or blurs the image. In short it is a measure of how much stars twinkle at the site.
Seeing is measured in terms of the smallest discernible detail in arcseconds. A good site will have seing of less than one arcsecond. The best Chilean sites have seeing that averages around 0.7 arcseconds at best. Mauna Kea can have seeing that averages around 0.4 arcseconds when it is good, roughly twice as good as Chile.
Only one other site on the planet routinely offers better seeing… South Dome Antartica, a good site, but one with a host of other problems… Six months of sunlight, with much of the dark winter featuring heavy cloud cover and raging storms. Never mind horrible access issues and a couple miles of ice over the site.
One measure of quality where Chile surpasses Mauna Kea is in low humidity. Water vapor in the air blocks some wavelengths of light from reaching a telescope on the surface. In this respect Mauna Kea is good, Chilean sites are superb. This is not as much of a concern in the optical and infrared where TMT is designed to operate, thus seeing is much more important in choosing a site for TMT.
It is also true that TMT will be equipped with an adaptive optics system that can improve the seeing of any given site on the planet. What many do not understand is that adaptive optics is not perfect and only improves upon an already good site. A mediocre site plus AO is good. A site with excellent seeing plus AO is superb.
It is true that TMT could be built in the Canary Islands or one of the other sites that was studied, but nowhere will yield the quality of data available at Mauna Kea.
Result: Partly True