Promise 1: By Airline To Country X. As a condition of flying into country X, the airline promises country X to remove you if you are refused. That is a promise to country X, not to you; in this transaction you are nothing but cargo.* This applies for any reason you are refused.
Promise 2: By You to the Airline. You promise that if you are refused, you will pay a fare for the abovementioned ride home.
Promise 3: By Airline To Country X. The airline will check your papers for the correct visa. For this, they face a fine if they do not comply.
Suppose your papers are fine, and the airline boards you. When you land, the Immigration Officer finds your papers are in order, but your business attire raises questions; you seem to be seeking employment and are refused. The airline 1) must fly you back, 2) you must pay the fare, and 3) the airline does not pay a fine because they did their part.
None of these promises are from the airline to you.