He does, but he doesn't present the belt. He can win it, but whether he keeps it is UFC's decision. If they strip him he can't overrule them and take it back. UFC is the authority on the titles it renders, not the fighters. If UFC wants, it can walk away from Conor, it's not incumbent upon him to make their life easier. Expecting anything else shows fundamental misunderstanding of markets. Conor owes nobody anything.
Let's try and simplify this mental exercise a bit. You happen to have a winning race horse that some guy you met wants to pay you $100,000,000/race, and you agree to it. You now have enough money that you don't need another race, but decide to stay open to the possibility just for shits and giggles, would you ask for less the next time around just because another guy wants to bargain and isn't immediately ready to meet your asking price? No, you would bargain until the price is met or gets close to it, or the negotiations break down and the other guy walks away, because there is no pressure on you - he came to you, not you to him, so he needs you more than you need his money.
Conor owes you and UFC nothing. UFC needs to make the decision about the belt, not Conor.