If that's a rule it was made up by people who hadn't considered the edge cases. If you're ending a sentence with a quote, and the appropriate punctuation marks are different for the quote and the sentence, then you should do whatever makes sense, with question marks trumping fullstops. For instance:

1. Did anyone else think "Battlestar was right"?

2. I thought "Battlestar was right."

3. I thought "Was Battlestar right?"

4. Did anyone else think "Was Battlestar right?"

Oh yes, and the relevant "rules" differ between American and British English anyway.

Limiting punctuation to inside or outside of the quotation marks always struck me as exceptionally archaic as it frequently overcomplicates a sentence.

You should punctuate the quotation as if the quote were independent. If the quotation is a question it should contain the question mark, it's only logical. A question without a question mark is punctuated incorrectly - that's just plain simple logic.

If I tell you that my wife just asked me, "Can you grab a drink?" The question mark has to be inside the quotes otherwise it becomes my question. I didn't ask myself the question, so why is my punctuation asking it? Plus an unpunctuated quotation looks ugly to me.