Some of the previous answers contain some very valid points, but they forget one very important factor: ALL REAL ESTATE LAWS VARY FROM STATE TO STATE. Sure there is a portion that applies accross the nation, but the nuances change in every state. In the state where I live and practice, items found deffective in an inspection do not have to be fixed by the seller. These defficencies do give the buyer a way out of their contract or possibly a means to renegotiate, but the seller is under no obligation to fix anything, only disclose what he knows.
As to the MLS situation/designation, this again depends on the contract that the seller has with his agent and the buyer as well as the practices and proceedures of the local MLS office. Maybe the proceedure in your area is that they continue to market the home until the close of escrow. This would include accepting back up offers,...
Now, regardless of where you are located, the seller can not unilatterally back out of the sale contract with you just because he received a better offer from someone else. If he does, then you could sue him for specific performance. However, if you change the contract in any way due to the results of the inspections (ask him to fix something not originally agreed to,...) the original contract is void. At that time he would be free to accept another offer.
The best thing is to contact your agent or his supervising broker if you have any questions. Because regardless of our intents, unless we see the actual contracts and agreements, there is no way to provide you with solid advice.