I haven't seen your contract and every contract has its own intricacies. But, in general, based on the contracts written up on NWMLS forms here in the Seattle area, a seller can almost never 'back out' of a deal. The contract states that it must close within 35 days. The bank is essentially giving one more week of leeway in case there are any last minute delays that take a day or two.
If the buyer or seller fails to perform and does not close the deal within the 35 day period as specified on the contract, then it is not a case of 'backing out.' The situation is that the contract is now failed (i don't know what the real legal term is) but the buyer and seller did not perform to the contract. So, it's done. That contract is thrown out the window and you move on. The additional week the bank is allowing has nothing to do with this situation unless the buyer and seller agree in writing to extend the closing date beyond the 35 days.
If the buyer and seller agree to extend the close 2-3 weeks more, even beyond the 1 week granted by the bank, that is fine. They can do that. It is still a binding contract between buyer and seller. But, they now longer have the bank's approval and the bank may refuse to remove the lien from the property which would prevent the property being transferred to the new buyer. They would have to get the bank to approve the extended close time frame. This happens regularly.
So, yes, the selling agent is right to push to close within the 35 day period or you have failed to perform to the contract. The bank's approval date is meaningless with regards to the contract that the buyer and seller have signed with each other.