It can, but you have to go wildly out of the norm for this to be so. Like, I have serious kidney issues, and I hate plain water. My nephrologist said me drinking 1-3 gallons of iced, and hot, tea per day is fine. The only time it becomes an issue is when you have have extremely concentrated black tea. Even then you would have to be drinking a lot of it, like a lot. He cautioned on tea mixes because those can add sodium, and of course not to use sugar, but that it would be little different than drinking water otherwise.
Tea contains oaxalates which are a main component of kidney stones. However, most studies indicate that you would have to drink a ridiculous amount of iced tea to cause stones to form. I think he probably just developed them through usual means, did a little internet research and convinced himself it's the tea.
Obviously this isn't OP, but that dude is cray cray, he loves Ice Tea so much that he doesn't mind cloggin up his own kidney and urethra, but more worried about some voodoo cleaner antics, that shit is crazy bro