This was pointed out by Newton after his investigation with prisms. A color can be the result of a single wavelength, or the combination of different lights with different wavelengths, called metameres (lights that look the same but are physically different). A solution was proposed by Young. He suggested that color metameres could be explained by a discrete number of light receptors with different wavelength sensitivity, which he accurately predicted to be threefold (therefore hypothesizing the existence of cones). Think of a single cone, like the S-cone from your graph. For a pure light at 420nm, the cone sensitivity is half its peak. If you change the wavelength of the light to 440, then the cone will essentially double its response. Now if you keep the light at 420 but double its intensity, the cone will also double its response. So you cannot perceive color based on a single cone, because based its response you couldn't tell the difference between a change in intensity (brightness) or color (chroma). For perceiving color, you need more than 1 cone, and what matters is the relative response between the cones. While the overall response tells you the how bright the object is (technically its looks like only the M and L cones contribute to brightness perception, but this is a detail). Now if you had cones with peak sensitivities randomly distributed (assuming a very large number of cones), there would never be ambiguity in what color is being presented, because you would always have a pair of cones that would have different responses. The fact that there are metameres tells you that this number of types of cones must be small. That's essentially Young's great intuition on the topic.
Later Maxwell tested this hypothesis explicitly. Think of it as a set of equations with N unknown. We know from the laws of arithmetic that you need N different equations to solve the unknown. Maxwell used that property in his color matching experiment. Basically he presented one color on one half of a field and built a device that allowed him to vary the intensity of 3 lights on the other half (technically one light was subtracted to the first half for experimental convenience, but the logic holds). He showed that using this device he could match any color displayed on the first half. But you cannot do that with only 2 lights. This demonstrates conclusively that there are 3 discrete types of cones in the eye. Using this technique it is even possible to build arbitrary color spaces, which is how the CIE XYZ color space was invented, even before we knew the true sensitivity function of the cones. That's the answer to your question: the only thing that matters is that the 2 lights additively stimulate cones the same way that the single pure light would. Your brain therefore cannot tell the difference, because all it "sees" is 3 numbers coming from 3 types of cones.
So metameres are sets of lights that stimulate the 3 cones with the same relative intensity. It means that what we perceive of colors is actually a very poor representation of the complexity of a light spectrum (even within the very narrow range of wavelengths we perceive). Yet it is also lucky, because it means that we can recreate any color using a combination of just 3 lights. Maxwell understood that and here again showed that he was not only the greatest theorist of his generation but also a brilliant experimentalist by taking 3 pictures of the same object behind colored filters. Then he back-projected the pictures using the same filters to demonstrate that he could recreate the color of the object. The actual demonstration didn't work very well, but the point is that he gave the key for the technology that is now in every single display on the planet: using 3 LEDS (RGB) to display colors. This is based on the aforementioned XYZ color space. If you take a picture based a filters that produce a given color matching function, you can then convert it to a display that has different filters as long as you measured the color matching function of this display. This color space (CIE XYZ) is really remarkable because even though its input is physical (intensity of a light at a given wavelength), the output is psychological (what color humans perceive). In facts this space is constructed based on an average observer. But, based on the fact that you perceive colors that seem at least broadly correct on many different displays, it works very well.