If someone can TIG weld then they can TIG weld titanium.
But how well shielded the weld puddle will be will depend on their experience and understanding of the requirements of an effective purge, to avoid contamination and degredation of the metal.
http://www.twi.co.uk/content/ksrjp002.html
“The titanium expert knows that it is one of the easiest materials to weld – but he is very familiar with very good back purges, and the use of a trailing shield.”
http://www.weldingtipsandtricks.com/welding-titanium.html
“You only get one shot with titanium “
Once the titanium (weld) has absorbed any oxygen, nitrogen or other contamination from the atmosphere then the damage is done. A bad weld can be dug out and redone but, only if it is done in a controlled environment.
Welds can be dug out (dig and tig) for example if there is some tungsten inclusion (which would show up in a radiograph). But a poor weld can look much like a good weld once the surface (evidence) has been removed.
http://www.kobelco.co.jp/english/titan/files/details.pdf page 5 (although it is almost impossible to weld titanium without some discolouration. It is experience that the is best guide to what is acceptable discolouration)