Can using a non Apple USB cable damage an iPhone? If I use a generic/aftermarket iPhone USB cable instead of the official Apple product, can it damage the iPhone?  A vendor at the mall said that high quality iPhone USB cables have a chip that regulates the charging current so it won't damage the device.  He said the cheaper cables don't have that capability. Doesn't sound very credible, so I wanted to double check.
They are generally safe to use.  And they don't have a chip (at least the ones I've used).

The charger itself may regulate the current, but the cable itself doesn't.  I've used a multitude of cables from a multitude of vendors over the years and I've never had a problem with damaging devices.   Build quality is a different matter.  Too cheap, and the cables inside can break.   Rare but does/can happen.