Your instructor probably shouldn't be saying such things. They clearly haven't bothered to actually find out the truth. What it comes down to is what the Good Samaritan Law is in the place that you are in. This varies in the US by state.
In Minnesota, for example
http://www.heartsafeam.com/files/Min...aritan_Act.pdf
This link has each individual US state's Good Samaritan Law:
http://www.heartsafeam.com/pages/faq_good_samaritan
This is pretty much the way the various Good Samaritan Acts work in most provinces in Canada. If you are acting as a Good Samaritan (out of the kindness of your heart - aka no duty of care), you are protected from liability, unless you do something really, really stupid ("acts in a willful and wanton or reckless manner in providing the care, advice, or assistance")
In places that don't have a specific Good Samaritan Law/Act/etc, it is governed under common law. Long story short, you are protected in most places, but would do well to know the law of the particular place you are in. Where you are more likely to run into trouble is if you do what your instructor suggested and run away in places (such as Quebec) where you are considered to have a legal obligation to help.
Having a first aid instructor say something like that really bothers me, because it falsely encourages the fear of litigation that prevents people from helping each other out. Sure, there are some people out there who may try to sue you for trying to help them if it doesn't work out perfectly, but the fact of the matter is that they will lose their case almost anywhere they try it.