There is a very strong difference in signal from someone telling me "I am an expert C programmer" compared to "I am an expert PHP programmer."
Leaving out the name of the programming language all together removes salient content without adding anything else of value. If I want to make your of your programming skills, I'll still need to ask "Okay, what languages?"
So, saying that "Calling oneself a C Programmer is like saying you're a Hammer Carpenter" is like saying when there is a choice between tool sets, the choice doesn't matter.