Where's the Source for This One?

We're all aware of the various stringencies in the Chareidi world. And yes, some of them are pretty extreme or odd. Sometimes they're also annoying for those of us who are trying to present a rational frum face to the world:
It appears the Eida Chareidis Modesty Committee is seeking to set new rules for shopping in Ramot Daled, whose rav, HaGaon HaRav Fuchs Shlita also serves on the Eida and is tied to Vishnitz.
Rav Fuchs is calling for two checkout lines at the neighborhood grocery store, one for men and women. The Rav is also calling on residents to do their “big shopping” towards the beginning of the week and not towards Shabbos as is the case today in the hope of limiting the crowd at in the isles at any one time.
But at least this time they're at least vaguely based on some real prohibition, such as modesty or limitations on public inter-gender contact.
This one, though, struck me as just plain weird:
Four students were expelled from the Tiferet Israel yeshiva in Jerusalem last week after it became known that they had obtained driver's licenses in violation of the yeshiva's rules.
The decision triggered a heated debate among the ultra-Orthodox public surrounding the question of the legitimacy of owning a license.
I mean, could someone point me to the makor in the Shulchan Aruch for this one please? I mean, the questions around this are obvious. First of all, there's no shortage of Chareidi drivers in Israel. Are they all breaking halachah? And if not, what makes it okay for them? Is it a yeshivah-specific rule to avoid the bochrim all driving to school? Or it is an extension of "anything new is forbidden by the Torah" since there were no cars in 18th century Hungary?