I have had black vinyl bras on my Corvettes and never had any such damage. But like Tom says, if not properly installed or left on indefinitely, they can do harm to paint. Just be sure it's on tightly and take it off when your trip is over.
On our MR2 Spyder, the entire front was painted, so a full covering vinyl bra would have done good. Our current tow vehicle a 2006 Liberty, it has a raw plastic bumper so it is less concerning. It's painted grille seems to be doing well, no rock chips at all after a number of towing trips. My wife loves the Groucho Marx hood deflector/protector. Personally, I despise it, but it's her daily driver.
Here is a pic of the same hood protector my wife's Liberty has....Hi Groucho!