I feel that Lakoff and Johnson are ultimately correct in identifying metaphor as an essential component of defining the sorts of qualitative implications that words have. Metaphors help us establish the essential nature of words and concepts as well as their secondary non-essential qualities (connotations). The metaphors that shape our reality are largely inheritances of our culture and traditions. Metaphors have great rhetorical power because they shape reality by highlighting certain features of an idea while hiding others. Politicians regularly appeal to metaphor by phrasing political maneuvers in terms of them, characterizing their policy on drugs as "at war" for example. Critical audiences would do best to question the depth and usage of metaphors, even commonly accepted conventional ones. It could be the case that the assumptions behind our uses of metaphor are entirely arbitrary or driven by cultural prejudices that do not accurately reflect reality.
Yet metaphors appear to speak to audiences beyond a purely cultural level. We have the potential to understand some metaphors that are unconventional or strange to us through reflection. One who lives in contemporary times does just that when attempting to decipher the similes and metaphors in Shakespeare, many of whose metaphors have fallen into historical obscurity or were never common and conventional metaphors to begin with. Nonetheless, these metaphors can resonate with the readers if they have the appearance of reflecting the actual conditions of reality to us. The foreign student's misinterpretation of the "solution to my problems" phrase reflects a situation where we may find a potentially unintended meaning that still accurately characterizes some other concept.
Though we have only touched on his student Aristotle, I find myself wondering what his (to our understanding) teacher, Plato, would have to say about the usage of metaphor. Plato's epistemological outlook is Idealism, meaning that he believes that abstract knowledge or pure concepts are the highest form of reality and the physical objects of the world are simply crude representations of this knowledge. Plato is famous for his criticism of both rhetoric and poetry due to their power to deceive and manipulate. Metaphors can be utilized in a similar manner. However, metaphors are also a potent means of becoming familiar with the essential characteristics of a concept through comparison. Plato himself depended regularly on metaphor, framing many of his most famous propositions in terms of them (The Cave). However, his usage of metaphors can not necessarily be interpreted as an endorsement of the practice as Plato engaged in a number of practices that he regarded as intellectually questionable, namely the practice of writing himself, which he decried as a tool of remembering but an eraser of memory.