I've been an on car brake lathe convert for some time. When used correctly, they can do a superior job. Some of the older on car brake lathes are next to impossible to use, and some even cause problems from a wierd pattern from chatter. But one of the newer lathes used by a reasonably competent mechanic that has been trained to use it provides superior results.
That said, properly used by a competent mechanic that has been properly trained, an off car lathe can also produce excellent results.
To claim that an on car lathe is the only way or that using an off car lathe will cause damage is just plain ignorant. Either of these two tools can provide excellent results. The best mechanics can choose which tool IS BEST FOR THAT APPLICATION.