As this diagram shows, the responses of the cones overlap,

I'm very aware of that as you'll see if you follow the 3rd link in this post.

This assumes that only one cone will respond to a specific frequency.

Okay. The "colors" through which each point would scintillate wouldn't be red, blue and green. But, assuming the light eminating from any given point source consisted of an unattentuated, pure frequency, then if what we percieve were in direct proportion to that pure frequency, then the points would scintillate as the focused light hit the three diferent types of cones. And the three colours through which they would scintillate would be the same for every source of that given frequency.

But that doesn't happen. In part because of the persistance of human vision which aggregates and averages the spectral responces of many individual cones of all three types over time. To quote from another link in that other post:

Any color on the CIE chromaticity diagram can be considered to be a mixture of the three CIE primaries, X,Y,Z. That mixture may be specified by three numbers X,Y,Z called tristimulus values.

The CIE primaries are not real colors, but convenient mathematical constructs.

Nevertheless, the tristimulus values X,Y,Z uniquely represent a perceivable hue, and different combinations of light wavelengths which gives the same set of tristimulus values will be indistinquishable in chromaticity to the human eye.

So, whilst there may be no adjacent bands of red and blue in the source spectrum, our perception of all hues (including "pure red" and "pure blue"), will have influences from the conal responses to incedental and coincident frequencies eminating from other sources over both space and time. Ie. We percieve pinks in a rainbow even though there are none there at the source.