Exactly so.
In my experience, you have very little to fear from undercutters. You may lose the odd customer, but in my view they are ones who would be looking for the first excuse to drop you anyway.
Customers are in the main very loyal, so if you are doing a job they are happy with, and they like you as a person, you won't have any problems, even if you charge more than the 'competition'.
My aim is to do an excellent job for a fair and realistic price, and take a little time to get to build a good relationship with customers. By doing this, I have found that, no matter what 'competition' may emerge, my customers remain loyal to me.
John.