Is Displaying Non-Western Objects in a Western Setting an Injustice?

Is it wrong to display non-Western cultural artifacts in the setting of a Western-style museum display? This is a question that I have been mulling over for some time now, actually since I took a class on Japanese art last semester. The Freer and Sackler Galleries have a well-curated and extensive collection of Asian art. But do the museums do an injustice to the artwork by displaying them in a Western-style building instead of, say, a pagoda? What is the effect of displaying non-Western art in a Western setting? Or the effect of displaying objects that were not intended to be "art" (devotional statues, articles of clothing, etc.) in a museum setting?

Last year, one of the most successful exhibitions at the Sackler Gallery was the Tibetan Shrine from the Alice S. Kandell Collection, which essentially recreated a Tibetan Buddhist shrine and displayed all the objects in the shrine as they would be placed for worship. The exhibition was very well-received and continues to receive acclaim. Was it perhaps because it provided visitors with a rare look into how the art objects were meant to be used and displayed?

I am very intrigued by the example set by the Sackler's Tibetan Shrine, and I wonder if other museums would follow this lead for the display of other artworks. Certainly such displays would be more educational for visitors - they would be able to see for themselves what kind of uses the objects had, instead of merely reading about them on labels or in catalogs. Of course it is much more cost-effective to display artwork in cases or on a wall. But is it worth spending more money on an exhibition if it will be displayed in a manner more loyal to its contents' original purposes?