I'm surprised nobody else has said this. Leverage?

United > ULCC

This is like putting on your application at Harvard (or Yale or Stanford) that you also have an offer at an awesome state school, and you'll go if they don't hurry up and admit you.

Do you really think they care? (They don't)

Don't screw around. If asked answer honestly but don't brag about owning silver when they are offering you gold.