In short, yes the provisions of FAR 15 (specifically table 15.2 within 15.408) apply in this scenario. Per these provisions, the contractor's proposal was submitted correctly. Not knowing the size of the contract, de-scoped work, etc. I do not know the impact of the rate change on your contract. However, if you run the scenario using both sets of rates it will produce a range for you to negotiate your settlement of this issue.
Addressing the "large amount of money and fee" you identified in your background information. It is readily apparent because the rates have dropped that the funds are sitting there. On final contract closeout, if there is money in this pot, it will be de-obligated and returned to the government coffers. On the flip side of this scenario, if the rates had gone up, and you settled closer to the current rates there would be money there to cover all actual charges at closeout.