Does 「你的中文是在哪里学的？」mean "How did you study Chinese?" or "Where did you study Chinese?"
中国人：你的中文是在哪里学的？
我：在北京语言大学学的。

Without other context, this dialogue indicates a normal conversation sequence. '在哪里' just means 'where'.
In some context, 你的中文是在哪里学的？ could be used as a rhetorical question.  The underlying meaning is 你的中文是在哪里学的？ (怎么这么差！)  In English, it could be something like from where have you learned such awful Chinese? In this case, they may not want you to answer it literally. And I guess you don't want to answer it at all.
Out of that specific context, 你的中文是在哪里学的？ is just a normal sentence and your answer is a proper one.
To me, 在哪里(where) doesn't mean 怎么(how) in any case. And your Chinese friend might say it out of certain context, in which you should use 怎么 other than 在哪里，otherwise he is plain wrong.
Edit:
Context is the key here.  你的中文是在哪里学的？could also imply someone's Chinese is very good and they want to know where they have learnt it.  But standing alone, we can't make any assumption about the context.  We should take it literally instead, unless OP can provide more context for analysis.