They are correct to be cautious when sending an SMS message to a customer. You can face some hefty fines if not done correctly.
We had to research this extensively before we integrated SMS sending into our CRM and iPhone and iPad apps. The main thing to remember is to always provide the customer with a STOP message for each and every single message you send out. We have to comply with some pretty strict opt out guidelines and provide the customer the ability to control if they receive any further messages.
We have had a dealer or two ask if we can change this for them (i.e. remove the opt out messages) and unfortunately, we had to let them know we were unable to do that for legal reasons. But, I think it's a win-win situation for everyone. The dealer still gets to send text messages their customers (which is an extremely effective form of communicating with customers) if the customer wants to receive it. And we (or whatever marketing/CRM tool you are using) protect the dealership from any legal liability in this area of marketing and communication.
I would say one thing for sure - be careful if you are texting back and forth with a customer outside of your CRM tool or another marketing tool that you use. If you are just texting them via your phone or a marketing tool that doesn't follow the guidelines from the FCC you could really open up your dealership to some large fines.
I am reminded of this story just last May:
How Avoid SMS/Texting Lawsuits: 4 Quick Tips to Keep Your Dealership Safe - Automotive Digital Marketing Professional Community
Late last year, a 2.5 million dollar lawsuit was won against Lithia Motors Inc. for sending unwanted text messages to customers without giving them the option to opt out of the text messages. According to AutoNews.com, Lithia was hit with a class-action lawsuit for broadcasting to 57,800 consumer cell phones text messages that failed to adequately allow the recipients to opt out of future texts. A second Lithia broadcast text went to 48,000 of the previous recipients, 6,190 of whom said that they tried to opt out but were unable to.
None of the above is meant to scare anyone away from texting their customers. However, just make sure you follow the guidelines and you should be ok.
We have seen wonderful results from the dealerships we have worked with to send and receive messages with their customers. Over 2,049 incoming messages within the last 4-5 months alone. That is incoming from customers - not outgoing. That lets us know that it is definitely a great tool to use if done properly. 
Doesn't matter if you use us or one of our competitors. I think we all want to be in the business of avoiding lawsuits.
