Ah, a good question. To answer this, you'd have to do three general things: you'd need to examine the different settings, determine if they influence your understanding of the action, and assemble your response into a logical structure.
If you look at how differently the characters act when they are in different settings, you'd have to say that this statement is not true, or at least not very true. Look at how wildly differently the young lovers act when they are still in the city in the daylight versus when they are in the woods and at night! They literally change who they love, how they act, etc. Likewise, Bottom doesn't change into anyone or anything else when he's at home in the town, but only in the woods.
So, move through each setting, looking at how the characters change, and you'll do well.