I see what you're saying. (C) is clearly the most defensible of the five choices, but to say that (C) is a "statement made in the passage" is a little strong.
Essentially, you're pointing out the middle ground between refusing something and embracing it. What about just a neutral feeling?
Just because jazz doesn't close itself off to other music, can we infer that it actively welcomes other music?
Even though I agree with you that there is space between "doesn't close off" and "embraces", the actual context and subject matter make those concepts closer than they would be in straight definitional terms.
That jazz has "never closed itself off" from other forms allows us to infer that jazz has "always remained open" to other forms of music. When we learn in lines 33-37 that some jazz has actively taken other musical forms (the European songs of US theater) and adapted them, we can certainly say that SOME jazz musicians have embraced other musical forms.
So the composite of those two ideas is close enough for them to defend (C), although I do agree with you that the question stem should be more softly worded to reflect that bit of paraphrasing (something like "is most supported by the passage" / "the passage suggests" ).
The rest of the world may hate nitpickers, but in the LSAT world, we respect them.