If people with colorblindness lack one type of cone cells, shouldn't they be unable to recognize one particular color?
Cones do not literally interpret colors.  The three cones work together to encode a signal that is abstractly interpreted by your brain in higher processing centers.  Here is what neuroscientists currently think the decoding scheme looks like:



This leads to what's called opponent process, an antagonist mechanism whereby the perception of green/red are a matter of the contrast between the two.  In a deuteranopes, the mechanism of antagonism is missing, so the colors can not be differentiated.

What this implies is that (to some extent) a single color has no meaning.  Colors are only meaningful in the context of other colors.