This information you received seems incorrect, most all states now share information regarding traffic tickets and if you fail to pay for a traffic ticket out of state. While in the past states may not have shared information or were slow to inform your home state of an unpaid ticket with the technological advances in the past several years the courts and DMVs can transmit information to each other easily and quickly.
South Carolina is part of both the Driver License Compact (DLC) and Non-Resident Violator Compact (NRVC). The DLC requires member states to report convictions for moving violation tickets received by motorists back to the state in which they are licensed. The home state then decides, depending upon their own state laws, if an out of state ticket will then go on the driver's record and assigned points. Many states do add it to the motor vehicle record of the driver and some assess points.
The NRVC requires member states to suspend the driver’s license of those who get traffic tickets for moving violations in other states and fails to pay or otherwise legally take care of the citation. So with this if you do not pay nor show up in court then the state in which you received the ticket would inform your licensing state that you had a failure to comply or failure to appear for your traffic ticket. Your home state should then suspend your license until the out of state ticket is dealt with properly.
Since SC is part of both of these multi-state agreements it is likely that your home state will be advised of the moving violation and will suspend your license if you fail to pay the ticket and just ignore it.
Even if your home state is not part of the DLC or NRVC they likely will be informed by the SC courts of your failure to pay for the ticket and may still place penalties on you, such as suspending your license. You are right that if you do not pay it that you should not drive in South Carolina because your license will likely be suspended in that state for failure to appear in court or pay for your traffic citation. But there can be other far-reaching consequences for not paying the SC ticket, such as the state of South Carolina sending your fine amount to collections.
You then could be hounded by a collection company and receive a black mark on your credit report for not paying this ticket and having to be sent to collections. Also if you do not pay on time then the fine amount normally continues to grow and late fees are added.
If you feel that the ticket for disobeying traffic in SC was not deserved you can try to fight it in court and try to win so that the $129 fine is not due and the charge is dismissed. If you instead choose to ignore the ticket then you may find that it will continue to follow you and may get your license suspended not only in SC but your home state as well.
To find out what you home state may do if you fail to pay this SC citation you can check with the Department of Motor Vehicles in your state.