I hit a nasty bolt dead center of the tire on my Ford Ranger truck. Sam's Club said they couldn't patch it because of the broken wires, but that someone else could probably plug it. Went to Discount Tire and they told me it was too big to repair. Went to Wal-Mart (expecting to just order a new tire) and they "fixed" it with a patch leaving the broken wires exposed. Should I be concerned about the pictured repair?
This damage is not acceptable. Water could get into the inner layers of the tire that contain the steel belts and corrode them which can lead to tread separation. Tread separation would result in tire failure that could lead to loss of control of the vehicle. Proper tire repair standards require that the hole be plugged to seal against water intrusion into the inner layers and belt area and that a surface patch be placed in the inner liner to seal the air leak. This is usually done with a "patch plug".
See industry tire repair standards here. Tire repair standards
Tire patch plug
The broken cord wires alone would disqualify this tire from further use. The further fact that the wire sticking out would cause a patch plug unit to not completely seal the hole, even if one had been used, seals the tires fate. This is the reason that the repair techs that rejected the repair did so. They have been properly trained. As you found there are still lots of techs who have not been properly trained or choose to perform inappropriate repairs.