This is a great example of a myth in the making due to poor reporting and science-by-case-report.
The report in question is just that-- a case report. It is not scientific in any sense. There's no way to establish causality here. All we can tell is this guy had oxalate kidney stones, and he also drank a lot of tea. That's it.
Controlled studies have found lower rates of kidney stones in tea drinkers:
And why iced tea in particular? That idea seems to have come from one single doctor, who said in an interview once that cold tea encourages people to drink more of it, versus hot tea. Again, no evidence, just cuz he thinks so:
The authors of that case report somehow miscalculated the oxlate content of tea by a factor of ten. They claim that tea contains 50-100mg of oxalate per 100 ml. The actual content is about a tenth of that. Much less than a host of other common foods. And of course their report makes attempt to ascertain the rest of his diet.