Memories are an interesting mixture of fact and feeling, which is one reason oral heirlooms are so valuable to a family's sense of self. And we don't mean the pretty version retold at ladies luncheons, either. Nearly every family has a skeleton in the closet (which is one reason genealogical finds can be so exciting). Whether it's an unexpected pregnancy or a murder trial set against a backdrop of the Roaring Twenties, odds are your family has a story that was never intended for public consumption.
And, while a few pointed questions may be met with resistance, you should also be prepared for the opposite effect. Don't be surprised if a family member decides to lighten their emotional load by telling you the whole truth.
That's also a good reason to do some legal research before adding all those question marks to the end of your sentences. Unless you plan to use only limited excerpts from your interview, which isn't really the point of documenting your family history, then you may need to have the subject sign a release form.
He or she could stipulate that parts of the interview remained closed, sometimes until after death.